ChemWiki - User contributions [en]

File:Endo opt sp.mol

2011-12-16T14:06:02Z

Sp3609:

Rep:Mod:sp33

2011-12-16T14:05:41Z

Sp3609: /* Malic anhydride + 1,3 Cyclohexadiene */

= Cope Rearrangement =
The cope rearrangement was discovered by A. Cope and E. Hardy in 1939<ref>A.Cope et al, ''J. Am. Chem. Soc.'', 1940, 62, 441-444 {{DOI|10.1021/ja01859a055}}</ref>The reaction is a [3,3] sigmatropic reaction that has been proven to occur concertedly.<ref>O. Wiest, A.Kersey, et. al; ''J. Am. Chem. Soc.''; 1994, '''116''', 10336-10337{{DOI|10.1021/ja00101a078}}</ref>
[[Image:copeschemesp.gif|300px| ]]

It is generally accepted that the reaction goes via a chair or boat like transition state.

[[Image:TSsp.gif|300px| ]]

The low-energy minima and transition structures on the C6H10 potential energy surface can be found, in order to determine the preferred reaction mechanism.

== optimising the reactant and product ==

A molecule of 1,5 hexadiene (1) was drawn using gaussian with an anti linkage of the main chain. It was then optimised using the HF/3-21G method and then the energy and symmetry were recorded in the table below. A gauche conformer (2) of the molecule was also optimised and analysed. The gauche conformer was lower in energy . In order to calculate the activation energies and enthalpies the lowest energy conformer is needed. Because the Gauche conformer is lower in energy, it would make sense to try structures with more gauche conformations in them. Several structures were tried to see which was lowest in energy. They were then identified by comparing to the low energy conformers in [[Mod:phys3#Appendix 1|Appendix 1]] .

{| class="wikitable" border="1"

! !! conformer !!Energy /a.u !! Energy /Kcalmol-1 !! Point Group !! Conformation
|-
| 1 || [[Image:conformer 1sp.jpeg|thumb|100px|<jmolFile text="Conformer 1">confomer1sp.mol</jmolFile> ]] || -231.69097 || -145388.28 || C1 || anti 4
|-
| 2 || [[Image:conformer 2sp.jpeg|thumb|100px|<jmolFile text="Conformer 2">confomer2sp.mol</jmolFile> ]]|| -231.68962 || -145387.43 || C1 || gauche 5
|-
| 3 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Conformer 3">confomer3sp.mol</jmolFile> ]] || -231.69260 || -145389.30 || C2 || anti 1
|-
| 4 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Conformer 4">confomer4sp.mol</jmolFile> ]] || -231.69266 || -145389.34 || C1 || gauche 3
|-
| 5 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Conformer 5">confomer5sp.mol</jmolFile> ]] || -231.69254 || -145389.26 || Ci || anti 2

|}

The lowest energy conformation is the gauche 3 conformation followed by the anti 1 conformation. The introduction of the gauche linkage means the molecule is more stable as there are now more favorable van der Waahls interactions.
The lowest three conformations were then optimised at the B3LYP/6-31G* level, as this is a more powerful technique and gives more accurate energies.

{| class="wikitable" border="1"

! conformer !! Energy /a.u !! Energy /Kcalmol-1 || input structure || output structure
|-
| Gauche 3|| -234.61133 || -147220.83 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">confomer4sp.mol</jmolFile> ]] || [[Image:gauche3sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">gauche3sp.mol</jmolFile> ]]
|-
| Anti 1 || -234.61179 || -147221.12 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Anti 1">confomer3sp.mol</jmolFile> ]] || [[Image:anti1sp.jpeg|thumb|100px|<jmolFile text="Anti 1">anti1sp.mol</jmolFile> ]]
|-
| Anti 2 || -234.61171 || -147221.07 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Anti 2">confomer5sp.mol</jmolFile> ]] || [[Image:anti2sp.jpeg|thumb|100px|<jmolFile text="Anti 2">anti2sp.mol</jmolFile> ]]
|}
When calculated at this higher level the energies of the three conformers change and the anti 1 conformer is now the lowest in energy. As can be seen from the images there isn't a large difference between the structures from the two levels of optimisation.

When the reaction occurs it goes from the Ci symmetry conformer. Therefore the geometries from the two calculations can be compared directly.

{| class="wikitable" border="1"

! method !! Bond lengths/Å and Angles /°
|-
| HF/3-21G ||[[Image:cibondsp.jpeg|400px| ]]
|-
| B3LYP/6-31G* ||[[Image:ci2bondssp.jpeg|400px| ]]
|}
The bond lengths are very similar but the angles are relatively different. with the B3LYP structure being slightly more linear.

The frequency analysis of this conformer was performed to ensure that a true minima had been found.
[[Image:IR anti2sp.jpeg|thumb|center|400px| Ci conformer ]]
As can be seen in the spectra, there are no negative vibrations, so it is confirmed that an actual minima has been found as oppose to a transition atate maxima.

The various energies of the system are also calculated using this method. The sum of the electronic and zero point energies is the potential energy at 0K. The sum of electronic and thermal energies gives the energy at 298.15K and 1 atmosphere. It contains contributions from the translational, rotational and vibrational energies. The third gives the enthalpy and takes into a correction for room temperature as H = E + RT. The fourth is the energy with the entropic contribution to the free energy considered. The final three are calculated at 298.15K and all energies are given in atomic units.

{| class="wikitable" border="1"

! !! a.u. !! kJmol-1
|-
| Sum of electronic and zero point energies || -234.469204 || -615599
|-
| Sum of electronic and thermal energies || -234.461857 || -615580
|-
| Sum of electronic and thermal enthalpies || -234.460913 || -615577
|-
| Sum of electronic and thermal free energies || -234.500777 || -615682
|}

Calculation files: https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Gauche_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_confomer_2nd.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Gauche_3rd_confomer.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_confomer_2_ci.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_3rd.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:2nd_gauche_confomer.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_2_freq_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti2_2nd_opt_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_2_freq_out.out

== Optimising the Transition States ==
=== Chair Transition States ===

To begin with an allyl fragment was optimised at the HF/3-21G level. Two of these fragments were then combined to give an initial structure for the chair T.S. The two fragments were placed with the ends of the allyl fragments 2.2Å apart and then optimised using in two different ways.

The first method calculates the force constant matriix in order to find the position of the T.S. The structure was optimised and the frequency analysis in one step.[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S 1">chair ts opt 1.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932246
|-
| RMS Gradient Norm /a.u.|| 0.00001378
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -818.97 which corresponds to the formation of one bond and breaking of the other.

[[Image:chairvib1sp.jpeg|300px| ]]

The second method uses a frozen co-ordinate method. The two allyl fragments were optimised with the two ends frozen at 2.2Å at the HF/3-21G level and then again with then bonds unfrozen. [[Image:chair ts otheropt part 2.jpeg|thumb|300px|<jmolFile text="Chair T.S 2">chair ts opt 2.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932189
|-
| RMS Gradient Norm /a.u.|| 0.00005807

|}

The geometries of the two optimised transition states are compared in the table below

{| class="wikitable" border="1"

! !! 1st Method || 2nd Method
|-
| C-C bond formed/broken || 2.02 || 2.02
|-
| other C-C bonds || 1.389 || 1.389
|}

They both give identical transition state geometries so either can be used depending on how much information about the transition state is known.

Calculation Data:https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ICR_OF_CHAIR.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ICR_CHAIR_2.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIT_TS_OTHER_OPT_PART_2.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIT_TS_OTHER_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIR_TS_GUESS_1_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIR_ICR.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIR_B3OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Chair_higher_opt_out.out

=== Boat Transition State ===
The Boat T.S was optimised using the QST2 method. This takes the reactant structure and product structure and extrapolates between the two, to find the transition state.The two structures were positioned so they are similar to a boat conformation and then optimised. [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat ts">QST2 opt.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60279992
|-
| RMS Gradient Norm /a.u.|| 0.00013432
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -840.35 which corresponds to the formation of one bond and breaking of the other.

[[Image:boat higher vib sp.jpeg|300px| ]]

The bonds that are being formed are 2.14Å and the other C-C bonds are 1.382Å.

Calculation Data: https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QST2_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:2ND_OPTIMISATION.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:2ND_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:1ST_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Boat_higher_opt_out.out

=== Intrinsic reaction co-ordinate ===

From looking at the transition states, its near on impossible to tell which conformer the reaction path will lead to. However using the IRC method the minimum energy path to the nearest minima can be followed. Because the reaction is symmetric it only needs to be run in the forward reaction.

This was initially done with 50 points along the pathway, however that didn't lead to a minima, so it was run again with 100 points.

{| class="wikitable" border="1"

! Points along the IRC !! Energy Graph !! RMS gradient Graph || Inital Structure || Final Structure
|-
| 50 || [[Image:chair icr 1 energy graph.jpeg|200px| ]] || [[Image:chair icr 1 rms graph.jpeg|200px| ]] || [[Image:icr 1 initial.jpeg|200px| ]] || [[Image:icr 1 final.jpeg|200px| ]]
|-
| 100 || [[Image:ICR 2 chair energy graph.jpeg|300px| ]] || [[Image:ICR 2 chair rms graph.jpeg|300px| ]] || [[Image:icr 2 initial.jpeg|200px| ]] || [[Image:icr 2 final.jpeg|200px| ]]
|}

As can be seen the gradient doesn't reach zero, even for 100 points, and the final structure is almost identical. In order to get further the force constants may need to be calculated at every step instead of just once.

== Calculating Activation Energies ==

To calculate the activation energies of the reaction via each transition state the transition states need to be optimised at a higher level to give more accurate energies. Therefore both were optimised at the B3LYP/6-31G* level.

{| class="wikitable" border="1"
|+ Chair T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure ||[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S ">chair ts opt 1.mol</jmolFile> ]] || [[Image:chair higher opt.jpeg|thumb|300px|<jmolFile text="Chair T.S">chair higher opt.mol</jmolFile> ]]
|-
| Energy || -231.619322 || -234.55698
|-
| new c-c bond lengths /Å || 2.02 || 1.97
|-
| other bond length /Å || 1.38 || 1.41
|-
| Frequency of imaginary vibration || -818.97 || -565.54
|}
{| class="wikitable" border="1"
|+ Boat T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure || [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">QST2 opt.mol</jmolFile> ]] || [[Image:boat higher opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">boat higher opt sp.mol</jmolFile> ]]
|-
| Energy || -231.602799 || -234.54309
|-
| new c-c bond lengths /Å || 2.14 || 2.21
|-
| other bond length /Å || 1.38 || 1.39
|-
| Frequency of imaginary vibration || -840.35 || -530.36
|}

As can be seen, the geometries are relatively similar but the energies are very different.
A summary of the energies is given below:

{| class="wikitable" border="1"

! !! Electronic energy !! Sum of electronic and zero point energies !! Sum of electronic and thermal energies !! Sum of electronic and thermal enthalpies !! Sum of electronic and thermal free energies
|-
| Reactant || -234.611710 || -234.469204 || -234.461857 || -234.460913 || -234.500777
|-
| Chair T.S || -234.556983 || -234.414929 || -234.409008 || -234.408064 || -234.443814
|-
| Boat T.S || -234.543093 || -234.402342 || -234.396008 || -234.395063 ||-234.431752
|}

The Activation Energy of the reaction can be calculated by Eactivation = Etransition state - Ereactants

To calcultate the Activation Energy at rooom temperature 298.15 K then the sum of the electronic and thermal energies should be used. To calculate it at 0K then the sum of electronic and zero point energies should be used.

Chair Transition State
@ 298.15 KEactivation = -234.409008- -234.461857 = 0.052849 au = 33.16 kcalmol-1
@ 0 KEactivation = -234.414929- -234.469204 = 0.054275 au = 34.06 kcalmol-1
Boat Transition State
@ 298.15 KEactivation = -234.396008- -234.461857 = 0.065849 au = 41.32 kcalmol-1
@ 0 KEactivation = -234.402342- -234.469204 = 0.066862 au = 41.96 kcalmol-1

The reaction that goes via a Chair Transition State has a lower activion energy and is therefore the way the reaction proceeds.

The experimental values for the activation energy via a chair transition state is 33.5 kcalmol-1 and via the boat transition state 44.7 kcalmol-1. The calculated values are in very close agreement with the experimental values.

= Diels-Alder Cycloaddition =
The Diels Alder reaction is a [4+2] cycloaddition. The reaction was discovered in 1928 by Otto Diels and Kurt Alder.<ref>Diels, O. Alder, K.; ''Justus Liebig's Annalen der Chemie''; 1928; '''460'''; 98–122.{{DOI|10.1002/jlac.19284600106}}</ref>
The reaction can be very stereo and regio specific depending on the elctronics and sterics of the reactants used.

Two different reactions will be looked at below:
1) the reaction between Cis butadiene and Ethene. This is the simplest Diels-Alder reaction possible, there are no side groups to influence the reaction sterically or electronicly, so the basics interactions of the reaction can be clearly seen.
2) the reaction between Malic anhydride + 1,3 Cyclohexadiene. This is more complex, as both the steric effect of the briding section and the electronic effect of the functionalised dienophile must be considered.

==Cis Butadiene and ethene ==

[[Image:butadiene reaction scheme sp.gif|thumb|widthpx| ]]

Cis butadiene was optimised at the HF/3-21G level.
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FOPT
|-
| Calculation Method ||RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -154.05394317
|-
| RMS Gradient Norm /a.u.|| 0.00007352
|}

The HOMO and LUMO were then calculated using the AM1 semi-empirical MO method.[[Image:butadiene plane sp.gif|thumb|200px|Plane of symmetry ]]

{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:butadiene homo sp.jpeg|200px]] || [[Image:butadiene lumo sp.jpeg|200px]]
|-
| Energy /a.u.|| -0.35083 || 0.01977
|-
| Symmetry || a || s
|}

The symmetry of the orbitals are determined with respect to the plane which runs through the center of the middle bond .
If the orbital is symmetric with respect to reflection in the plane, then it is labeled s and if not it is labeled a.

The transition state for the reaction has an envelope-like structure. It was drawn in gaussview with the ends of the two fragments positioned 2.2Å apart. The transition structure was optimised using at the HF/3-21G level using the QST2 method.
[[Image:transition state sp.jpeg|thumb|200px|<jmolFile text="Butadiene + ethene T.S">TS sp3609.mol</jmolFile> ]]
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60320837
|-
| RMS Gradient Norm /a.u.|| 0.00002624
|-
| Imaginary frequencies || 1
|}

[[Image:transition state geometry sp.jpeg|200px| ]]

The various bond lengths and angels of the transition state are detailed above. Typical sp3 c-c bonds are ~1.54Å and sp2 c-c bonds are ~1.33Å. The Van der Waahls radius of carbon is 1.70Å<ref>A. Bondi; ''J. Phys. Chem.'', 1964, '''68 (3)''', pp441–451 {{DOI|10.1021/j100785a001}}</ref> The σ bonds that are long compared to a σ bond, but the bonds in the cis butadiene are all approximately equal. This suggests that the starting point of the change in structure is a change in the electronic structure rather than the formation of new bonds.

[[Image:transition vibration sp.jpeg|thumb|100px| ]]The imaginary frequency occurs at -818.34 and corresponds to the formation of two new bonds in a synchronous fashion. As the new bonds form, the double bonds lengthen and the single bond in the butadiene contracts, which corresponds to the geometric changes that occur in the reaction. The lowest positive frequency occurs at 116.73 and corresponds to an asychronus movement of the two ethene carons towards the butadiene ends.

In order to ensure that the transition state had been found the IRC method was used to find the minimum energy pathway to the local minima, which should be the product.
The initial structure looks like the starting material and then the final structure looks like the transition state.

[[Image:ICR butadiene energy graph sp.jpeg|400px| ]][[Image:ICR butadiene rms graph sp.jpeg|400pxpx| ]]

[[Image:ICR initial structure butadiene sp.jpeg|thumb|left|200px|Initial Structure| ]][[Image:ICR final structure butadiene sp.jpeg|thumb|center|200pxpx|Final Structure| ]]

The Molecular orbitals of the transition state were calculated using the AM1 semi-empirical method. The symmetry was determined with respect to the plane of symmetry detailed above.
{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:TS homo sp.jpeg|200px]] || [[Image:TS lumo sp.jpeg|200px]]
|-
| Energy /a.u. || -0.32593 || 0.01842
|-
| Symmetry ||a || s
|}

The HOMO of ethene is the пc-c orbital which has s symmetry and the LUMO is the п*c-c orbital, which has a symmetry. The orbitals of ethene and butadiene can only interact if they have the same symmetry label. Therefore it can be seen that the HOMO of the transition state is made of the HOMO of butadiene and the LUMO of ethene and therefore is antisymmetric. And the LUMO of the transition state is made of the LUMO of butadiene and the HOMO of ethene and is symmetric. The reaction is allowed because the HOMO/LUMO pairs interact and are of similar sizes, so there is significant overlap.

Calculation Data: https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QST2_TS_OPT_BUTADIENE_3.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CIS_BUTADIENE_MO_AM1.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CIS_BUTADIENE_INITIAL_OPTIMISATION.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ICR_3_from_scan.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:MOS_OF_TRANSITION_STATE.LOG

== Malic anhydride + 1,3 Cyclohexadiene ==

[[Image:reaction scheme sp.gif|200px| reaction between malic anhydride + 1,3 cyclohexadiene ]]
The reaction between malic anhydride + 1,3 cyclohexadiene forms mainly the endo product, the reaction is presumed to be kinetically controlled. This can be confirmed by comparing the energies of the transition states.

In order to find the transition states both reactants were optimised at the HF/3-12G level.
{| class="wikitable" border="1"
|+ Optimisation summary
! heading !! Maleic Anhydride || 1,3 Cyclohexadiene
|-
| || [[Image:MA sp.jpeg|thumb|200px|<jmolFile text="Maleic Anhydride">MA sp.mol</jmolFile> ]] ||[[Image:cyclo sp.jpeg|thumb|200px|<jmolFile text="1,3 Cyclohexadiene">cyclo sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -375.10351323 || -230.54323110
|-
| RMS Gradient Norm /a.u.|| 0.00012414 || 0.00004255
|}

The Exo and Endo transition states were optimised by calulating the hessian.
{| class="wikitable" border="1"
|+ Optimisation summary
! !! Exo TS || Endo TS
|-
| || [[Image:exo ts sp3609.jpeg|thumb|200px|<jmolFile text="Exo TS">exo opt sp.mol</jmolFile> ]] || [[Image:endo ts sp3609.jpeg|thumb|200px|<jmolFile text="Endo TS">endo opt sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -605.60359122 || -605.61036815
|-
| RMS Gradient Norm /a.u.|| 0.00001656 || 0.00003160
|}

As can be seen the Exo transition state is higher in energy and so as the endo product is the one that is formed then it can be presumed that the reaction is kinetically controlled. Kinetically controlled reactions go via the lowest energy transition state regardless of whether or not it leads to the lowest energy product. It is generally considered that the stability of the endo transition state is due to steric effects destabilising the exo form and secondary orbital overlap stabilising the endo form.

[[Image:exo ts vib sp.jpeg|left|thumb|200px| Exo TS ]][[Image:endo ts vib sp.jpeg|center|thumb|200px|Endo TS]]
The frequency analysis for both was calculated and the imaginary frequency for the exo t.s. occurs at -647.33 ant for the endo t.s it occurs at -643.57. For both the vibration correspond with the synchronous formation of two bonds between the fragments.

The geometries of the the two structures are given below:

{| class="wikitable" border="1"
| Exo || Endo
|-
| [[Image:exo ts geom sp.jpeg|400px| ]] ||[[Image:endo ts geom sp.jpeg|400px| ]]
|-
| [[Image:exo o geom sp.jpeg|400px| ]] ||[[Image:endo o geom sp.jpeg|400px| ]]
|}
As can be seen both of the geometries are very similar, all the bond lengths ae more or less the same, the only diffenece is the orientation of the two fragments. However in the exo form there may be more steric strain as the hydrogens for the cyclohexadiene are closer to the maleic anhydride. As can be seen in the second pictures the exo form suffers some steric strain as the hydrogens of the CH2-CH2 bringe are close to the malic anhydride. The endo form deosn't sufffer this strain as much as the bridging portion is the double bond CH-CH section, so the hydrogens are further away.

In order to explore the secondary orbtial overlap, the molecular orbitals of the system were calculated using the AM1 semi-empirical method.

{| class="wikitable" border="1"

! !! Exo TS !! !! Endo TS !!
|-
| || HOMO || LUMO || HOMO || LUMO
|-
| ||[[Image:exo homo sp3609.jpeg|200px| ]] || [[Image:exo lumo sp3609.jpeg|200px| ]] ||[[Image:endo homo sp3609.jpeg|200px| ]] || [[Image:endo lumo sp3609.jpeg|200px| ]]
|-
|Energy /a.u|| -0.34113 || -0.04051 || -0.34321 || -0.03567
|}

The HOMO of the endo TS is lower in energy than that of the exo TS. In the endo conformer the p orbitals of the oxygen are in the same region as the π systems. This means that there is an opportunity for mixing, which lowers the energy of the HOMO, stabilising the system. In the exo form the p orbitals of the oxygen are seperated from the π system, so there is no chance of them interacting.

Calculation Data:https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:DIENE_INITIAL_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ANHYDRIDE_INITIAL_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Exo_opt_1_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:EXO_MOS_1.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ENDO_MOS_1.LOG

= References =
<references />

File:ENDO MOS 1.LOG

2011-12-16T14:04:40Z

Sp3609:

File:EXO MOS 1.LOG

2011-12-16T14:04:39Z

Sp3609:

File:Exo opt 1 out.out

2011-12-16T14:04:39Z

Sp3609:

File:ANHYDRIDE INITIAL OPT.LOG

2011-12-16T14:04:38Z

Sp3609:

File:DIENE INITIAL OPT.LOG

2011-12-16T14:04:37Z

Sp3609:

Rep:Mod:sp33

2011-12-16T14:02:45Z

Sp3609: /* Cis Butadiene and ethene */

File:MOS OF TRANSITION STATE.LOG

2011-12-16T14:02:30Z

Sp3609:

File:ICR 3 from scan.out

2011-12-16T14:01:29Z

Sp3609:

File:CIS BUTADIENE INITIAL OPTIMISATION.LOG

2011-12-16T14:01:29Z

Sp3609:

File:CIS BUTADIENE MO AM1.LOG

2011-12-16T14:01:29Z

Sp3609:

File:QST2 TS OPT BUTADIENE 3.LOG

2011-12-16T14:01:28Z

Sp3609:

Rep:Mod:sp33

2011-12-16T13:59:15Z

Sp3609: /* Boat Transition State */

= Cope Rearrangement =
The cope rearrangement was discovered by A. Cope and E. Hardy in 1939<ref>A.Cope et al, ''J. Am. Chem. Soc.'', 1940, 62, 441-444 {{DOI|10.1021/ja01859a055}}</ref>The reaction is a [3,3] sigmatropic reaction that has been proven to occur concertedly.<ref>O. Wiest, A.Kersey, et. al; ''J. Am. Chem. Soc.''; 1994, '''116''', 10336-10337{{DOI|10.1021/ja00101a078}}</ref>
[[Image:copeschemesp.gif|300px| ]]

It is generally accepted that the reaction goes via a chair or boat like transition state.

[[Image:TSsp.gif|300px| ]]

The low-energy minima and transition structures on the C6H10 potential energy surface can be found, in order to determine the preferred reaction mechanism.

== optimising the reactant and product ==

A molecule of 1,5 hexadiene (1) was drawn using gaussian with an anti linkage of the main chain. It was then optimised using the HF/3-21G method and then the energy and symmetry were recorded in the table below. A gauche conformer (2) of the molecule was also optimised and analysed. The gauche conformer was lower in energy . In order to calculate the activation energies and enthalpies the lowest energy conformer is needed. Because the Gauche conformer is lower in energy, it would make sense to try structures with more gauche conformations in them. Several structures were tried to see which was lowest in energy. They were then identified by comparing to the low energy conformers in [[Mod:phys3#Appendix 1|Appendix 1]] .

{| class="wikitable" border="1"

! !! conformer !!Energy /a.u !! Energy /Kcalmol-1 !! Point Group !! Conformation
|-
| 1 || [[Image:conformer 1sp.jpeg|thumb|100px|<jmolFile text="Conformer 1">confomer1sp.mol</jmolFile> ]] || -231.69097 || -145388.28 || C1 || anti 4
|-
| 2 || [[Image:conformer 2sp.jpeg|thumb|100px|<jmolFile text="Conformer 2">confomer2sp.mol</jmolFile> ]]|| -231.68962 || -145387.43 || C1 || gauche 5
|-
| 3 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Conformer 3">confomer3sp.mol</jmolFile> ]] || -231.69260 || -145389.30 || C2 || anti 1
|-
| 4 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Conformer 4">confomer4sp.mol</jmolFile> ]] || -231.69266 || -145389.34 || C1 || gauche 3
|-
| 5 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Conformer 5">confomer5sp.mol</jmolFile> ]] || -231.69254 || -145389.26 || Ci || anti 2

|}

The lowest energy conformation is the gauche 3 conformation followed by the anti 1 conformation. The introduction of the gauche linkage means the molecule is more stable as there are now more favorable van der Waahls interactions.
The lowest three conformations were then optimised at the B3LYP/6-31G* level, as this is a more powerful technique and gives more accurate energies.

{| class="wikitable" border="1"

! conformer !! Energy /a.u !! Energy /Kcalmol-1 || input structure || output structure
|-
| Gauche 3|| -234.61133 || -147220.83 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">confomer4sp.mol</jmolFile> ]] || [[Image:gauche3sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">gauche3sp.mol</jmolFile> ]]
|-
| Anti 1 || -234.61179 || -147221.12 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Anti 1">confomer3sp.mol</jmolFile> ]] || [[Image:anti1sp.jpeg|thumb|100px|<jmolFile text="Anti 1">anti1sp.mol</jmolFile> ]]
|-
| Anti 2 || -234.61171 || -147221.07 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Anti 2">confomer5sp.mol</jmolFile> ]] || [[Image:anti2sp.jpeg|thumb|100px|<jmolFile text="Anti 2">anti2sp.mol</jmolFile> ]]
|}
When calculated at this higher level the energies of the three conformers change and the anti 1 conformer is now the lowest in energy. As can be seen from the images there isn't a large difference between the structures from the two levels of optimisation.

When the reaction occurs it goes from the Ci symmetry conformer. Therefore the geometries from the two calculations can be compared directly.

{| class="wikitable" border="1"

! method !! Bond lengths/Å and Angles /°
|-
| HF/3-21G ||[[Image:cibondsp.jpeg|400px| ]]
|-
| B3LYP/6-31G* ||[[Image:ci2bondssp.jpeg|400px| ]]
|}
The bond lengths are very similar but the angles are relatively different. with the B3LYP structure being slightly more linear.

The frequency analysis of this conformer was performed to ensure that a true minima had been found.
[[Image:IR anti2sp.jpeg|thumb|center|400px| Ci conformer ]]
As can be seen in the spectra, there are no negative vibrations, so it is confirmed that an actual minima has been found as oppose to a transition atate maxima.

The various energies of the system are also calculated using this method. The sum of the electronic and zero point energies is the potential energy at 0K. The sum of electronic and thermal energies gives the energy at 298.15K and 1 atmosphere. It contains contributions from the translational, rotational and vibrational energies. The third gives the enthalpy and takes into a correction for room temperature as H = E + RT. The fourth is the energy with the entropic contribution to the free energy considered. The final three are calculated at 298.15K and all energies are given in atomic units.

{| class="wikitable" border="1"

! !! a.u. !! kJmol-1
|-
| Sum of electronic and zero point energies || -234.469204 || -615599
|-
| Sum of electronic and thermal energies || -234.461857 || -615580
|-
| Sum of electronic and thermal enthalpies || -234.460913 || -615577
|-
| Sum of electronic and thermal free energies || -234.500777 || -615682
|}

Calculation files: https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Gauche_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_confomer_2nd.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Gauche_3rd_confomer.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_confomer_2_ci.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_3rd.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:2nd_gauche_confomer.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_2_freq_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti2_2nd_opt_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_2_freq_out.out

== Optimising the Transition States ==
=== Chair Transition States ===

To begin with an allyl fragment was optimised at the HF/3-21G level. Two of these fragments were then combined to give an initial structure for the chair T.S. The two fragments were placed with the ends of the allyl fragments 2.2Å apart and then optimised using in two different ways.

The first method calculates the force constant matriix in order to find the position of the T.S. The structure was optimised and the frequency analysis in one step.[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S 1">chair ts opt 1.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932246
|-
| RMS Gradient Norm /a.u.|| 0.00001378
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -818.97 which corresponds to the formation of one bond and breaking of the other.

[[Image:chairvib1sp.jpeg|300px| ]]

The second method uses a frozen co-ordinate method. The two allyl fragments were optimised with the two ends frozen at 2.2Å at the HF/3-21G level and then again with then bonds unfrozen. [[Image:chair ts otheropt part 2.jpeg|thumb|300px|<jmolFile text="Chair T.S 2">chair ts opt 2.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932189
|-
| RMS Gradient Norm /a.u.|| 0.00005807

|}

The geometries of the two optimised transition states are compared in the table below

{| class="wikitable" border="1"

! !! 1st Method || 2nd Method
|-
| C-C bond formed/broken || 2.02 || 2.02
|-
| other C-C bonds || 1.389 || 1.389
|}

They both give identical transition state geometries so either can be used depending on how much information about the transition state is known.

Calculation Data:https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ICR_OF_CHAIR.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ICR_CHAIR_2.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIT_TS_OTHER_OPT_PART_2.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIT_TS_OTHER_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIR_TS_GUESS_1_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIR_ICR.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIR_B3OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Chair_higher_opt_out.out

=== Boat Transition State ===
The Boat T.S was optimised using the QST2 method. This takes the reactant structure and product structure and extrapolates between the two, to find the transition state.The two structures were positioned so they are similar to a boat conformation and then optimised. [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat ts">QST2 opt.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60279992
|-
| RMS Gradient Norm /a.u.|| 0.00013432
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -840.35 which corresponds to the formation of one bond and breaking of the other.

[[Image:boat higher vib sp.jpeg|300px| ]]

The bonds that are being formed are 2.14Å and the other C-C bonds are 1.382Å.

Calculation Data: https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:QST2_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:2ND_OPTIMISATION.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:2ND_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:1ST_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Boat_higher_opt_out.out

=== Intrinsic reaction co-ordinate ===

From looking at the transition states, its near on impossible to tell which conformer the reaction path will lead to. However using the IRC method the minimum energy path to the nearest minima can be followed. Because the reaction is symmetric it only needs to be run in the forward reaction.

This was initially done with 50 points along the pathway, however that didn't lead to a minima, so it was run again with 100 points.

{| class="wikitable" border="1"

! Points along the IRC !! Energy Graph !! RMS gradient Graph || Inital Structure || Final Structure
|-
| 50 || [[Image:chair icr 1 energy graph.jpeg|200px| ]] || [[Image:chair icr 1 rms graph.jpeg|200px| ]] || [[Image:icr 1 initial.jpeg|200px| ]] || [[Image:icr 1 final.jpeg|200px| ]]
|-
| 100 || [[Image:ICR 2 chair energy graph.jpeg|300px| ]] || [[Image:ICR 2 chair rms graph.jpeg|300px| ]] || [[Image:icr 2 initial.jpeg|200px| ]] || [[Image:icr 2 final.jpeg|200px| ]]
|}

As can be seen the gradient doesn't reach zero, even for 100 points, and the final structure is almost identical. In order to get further the force constants may need to be calculated at every step instead of just once.

== Calculating Activation Energies ==

To calculate the activation energies of the reaction via each transition state the transition states need to be optimised at a higher level to give more accurate energies. Therefore both were optimised at the B3LYP/6-31G* level.

{| class="wikitable" border="1"
|+ Chair T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure ||[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S ">chair ts opt 1.mol</jmolFile> ]] || [[Image:chair higher opt.jpeg|thumb|300px|<jmolFile text="Chair T.S">chair higher opt.mol</jmolFile> ]]
|-
| Energy || -231.619322 || -234.55698
|-
| new c-c bond lengths /Å || 2.02 || 1.97
|-
| other bond length /Å || 1.38 || 1.41
|-
| Frequency of imaginary vibration || -818.97 || -565.54
|}
{| class="wikitable" border="1"
|+ Boat T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure || [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">QST2 opt.mol</jmolFile> ]] || [[Image:boat higher opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">boat higher opt sp.mol</jmolFile> ]]
|-
| Energy || -231.602799 || -234.54309
|-
| new c-c bond lengths /Å || 2.14 || 2.21
|-
| other bond length /Å || 1.38 || 1.39
|-
| Frequency of imaginary vibration || -840.35 || -530.36
|}

As can be seen, the geometries are relatively similar but the energies are very different.
A summary of the energies is given below:

{| class="wikitable" border="1"

! !! Electronic energy !! Sum of electronic and zero point energies !! Sum of electronic and thermal energies !! Sum of electronic and thermal enthalpies !! Sum of electronic and thermal free energies
|-
| Reactant || -234.611710 || -234.469204 || -234.461857 || -234.460913 || -234.500777
|-
| Chair T.S || -234.556983 || -234.414929 || -234.409008 || -234.408064 || -234.443814
|-
| Boat T.S || -234.543093 || -234.402342 || -234.396008 || -234.395063 ||-234.431752
|}

The Activation Energy of the reaction can be calculated by Eactivation = Etransition state - Ereactants

To calcultate the Activation Energy at rooom temperature 298.15 K then the sum of the electronic and thermal energies should be used. To calculate it at 0K then the sum of electronic and zero point energies should be used.

Chair Transition State
@ 298.15 KEactivation = -234.409008- -234.461857 = 0.052849 au = 33.16 kcalmol-1
@ 0 KEactivation = -234.414929- -234.469204 = 0.054275 au = 34.06 kcalmol-1
Boat Transition State
@ 298.15 KEactivation = -234.396008- -234.461857 = 0.065849 au = 41.32 kcalmol-1
@ 0 KEactivation = -234.402342- -234.469204 = 0.066862 au = 41.96 kcalmol-1

The reaction that goes via a Chair Transition State has a lower activion energy and is therefore the way the reaction proceeds.

The experimental values for the activation energy via a chair transition state is 33.5 kcalmol-1 and via the boat transition state 44.7 kcalmol-1. The calculated values are in very close agreement with the experimental values.

= Diels-Alder Cycloaddition =
The Diels Alder reaction is a [4+2] cycloaddition. The reaction was discovered in 1928 by Otto Diels and Kurt Alder.<ref>Diels, O. Alder, K.; ''Justus Liebig's Annalen der Chemie''; 1928; '''460'''; 98–122.{{DOI|10.1002/jlac.19284600106}}</ref>
The reaction can be very stereo and regio specific depending on the elctronics and sterics of the reactants used.

Two different reactions will be looked at below:
1) the reaction between Cis butadiene and Ethene. This is the simplest Diels-Alder reaction possible, there are no side groups to influence the reaction sterically or electronicly, so the basics interactions of the reaction can be clearly seen.
2) the reaction between Malic anhydride + 1,3 Cyclohexadiene. This is more complex, as both the steric effect of the briding section and the electronic effect of the functionalised dienophile must be considered.

==Cis Butadiene and ethene ==

[[Image:butadiene reaction scheme sp.gif|thumb|widthpx| ]]

Cis butadiene was optimised at the HF/3-21G level.
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FOPT
|-
| Calculation Method ||RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -154.05394317
|-
| RMS Gradient Norm /a.u.|| 0.00007352
|}

The HOMO and LUMO were then calculated using the AM1 semi-empirical MO method.[[Image:butadiene plane sp.gif|thumb|200px|Plane of symmetry ]]

{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:butadiene homo sp.jpeg|200px]] || [[Image:butadiene lumo sp.jpeg|200px]]
|-
| Energy /a.u.|| -0.35083 || 0.01977
|-
| Symmetry || a || s
|}

The symmetry of the orbitals are determined with respect to the plane which runs through the center of the middle bond .
If the orbital is symmetric with respect to reflection in the plane, then it is labeled s and if not it is labeled a.

The transition state for the reaction has an envelope-like structure. It was drawn in gaussview with the ends of the two fragments positioned 2.2Å apart. The transition structure was optimised using at the HF/3-21G level using the QST2 method.
[[Image:transition state sp.jpeg|thumb|200px|<jmolFile text="Butadiene + ethene T.S">TS sp3609.mol</jmolFile> ]]
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60320837
|-
| RMS Gradient Norm /a.u.|| 0.00002624
|-
| Imaginary frequencies || 1
|}

[[Image:transition state geometry sp.jpeg|200px| ]]

The various bond lengths and angels of the transition state are detailed above. Typical sp3 c-c bonds are ~1.54Å and sp2 c-c bonds are ~1.33Å. The Van der Waahls radius of carbon is 1.70Å<ref>A. Bondi; ''J. Phys. Chem.'', 1964, '''68 (3)''', pp441–451 {{DOI|10.1021/j100785a001}}</ref> The σ bonds that are long compared to a σ bond, but the bonds in the cis butadiene are all approximately equal. This suggests that the starting point of the change in structure is a change in the electronic structure rather than the formation of new bonds.

[[Image:transition vibration sp.jpeg|thumb|100px| ]]The imaginary frequency occurs at -818.34 and corresponds to the formation of two new bonds in a synchronous fashion. As the new bonds form, the double bonds lengthen and the single bond in the butadiene contracts, which corresponds to the geometric changes that occur in the reaction. The lowest positive frequency occurs at 116.73 and corresponds to an asychronus movement of the two ethene carons towards the butadiene ends.

In order to ensure that the transition state had been found the IRC method was used to find the minimum energy pathway to the local minima, which should be the product.
The initial structure looks like the starting material and then the final structure looks like the transition state.

[[Image:ICR butadiene energy graph sp.jpeg|400px| ]][[Image:ICR butadiene rms graph sp.jpeg|400pxpx| ]]

[[Image:ICR initial structure butadiene sp.jpeg|thumb|left|200px|Initial Structure| ]][[Image:ICR final structure butadiene sp.jpeg|thumb|center|200pxpx|Final Structure| ]]

The Molecular orbitals of the transition state were calculated using the AM1 semi-empirical method. The symmetry was determined with respect to the plane of symmetry detailed above.
{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:TS homo sp.jpeg|200px]] || [[Image:TS lumo sp.jpeg|200px]]
|-
| Energy /a.u. || -0.32593 || 0.01842
|-
| Symmetry ||a || s
|}

The HOMO of ethene is the пc-c orbital which has s symmetry and the LUMO is the п*c-c orbital, which has a symmetry. The orbitals of ethene and butadiene can only interact if they have the same symmetry label. Therefore it can be seen that the HOMO of the transition state is made of the HOMO of butadiene and the LUMO of ethene and therefore is antisymmetric. And the LUMO of the transition state is made of the LUMO of butadiene and the HOMO of ethene and is symmetric. The reaction is allowed because the HOMO/LUMO pairs interact and are of similar sizes, so there is significant overlap.

== Malic anhydride + 1,3 Cyclohexadiene ==

[[Image:reaction scheme sp.gif|200px| reaction between malic anhydride + 1,3 cyclohexadiene ]]
The reaction between malic anhydride + 1,3 cyclohexadiene forms mainly the endo product, the reaction is presumed to be kinetically controlled. This can be confirmed by comparing the energies of the transition states.

In order to find the transition states both reactants were optimised at the HF/3-12G level.
{| class="wikitable" border="1"
|+ Optimisation summary
! heading !! Maleic Anhydride || 1,3 Cyclohexadiene
|-
| || [[Image:MA sp.jpeg|thumb|200px|<jmolFile text="Maleic Anhydride">MA sp.mol</jmolFile> ]] ||[[Image:cyclo sp.jpeg|thumb|200px|<jmolFile text="1,3 Cyclohexadiene">cyclo sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -375.10351323 || -230.54323110
|-
| RMS Gradient Norm /a.u.|| 0.00012414 || 0.00004255
|}

The Exo and Endo transition states were optimised by calulating the hessian.
{| class="wikitable" border="1"
|+ Optimisation summary
! !! Exo TS || Endo TS
|-
| || [[Image:exo ts sp3609.jpeg|thumb|200px|<jmolFile text="Exo TS">exo opt sp.mol</jmolFile> ]] || [[Image:endo ts sp3609.jpeg|thumb|200px|<jmolFile text="Endo TS">endo opt sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -605.60359122 || -605.61036815
|-
| RMS Gradient Norm /a.u.|| 0.00001656 || 0.00003160
|}

As can be seen the Exo transition state is higher in energy and so as the endo product is the one that is formed then it can be presumed that the reaction is kinetically controlled. Kinetically controlled reactions go via the lowest energy transition state regardless of whether or not it leads to the lowest energy product. It is generally considered that the stability of the endo transition state is due to steric effects destabilising the exo form and secondary orbital overlap stabilising the endo form.

[[Image:exo ts vib sp.jpeg|left|thumb|200px| Exo TS ]][[Image:endo ts vib sp.jpeg|center|thumb|200px|Endo TS]]
The frequency analysis for both was calculated and the imaginary frequency for the exo t.s. occurs at -647.33 ant for the endo t.s it occurs at -643.57. For both the vibration correspond with the synchronous formation of two bonds between the fragments.

The geometries of the the two structures are given below:

{| class="wikitable" border="1"
| Exo || Endo
|-
| [[Image:exo ts geom sp.jpeg|400px| ]] ||[[Image:endo ts geom sp.jpeg|400px| ]]
|-
| [[Image:exo o geom sp.jpeg|400px| ]] ||[[Image:endo o geom sp.jpeg|400px| ]]
|}
As can be seen both of the geometries are very similar, all the bond lengths ae more or less the same, the only diffenece is the orientation of the two fragments. However in the exo form there may be more steric strain as the hydrogens for the cyclohexadiene are closer to the maleic anhydride. As can be seen in the second pictures the exo form suffers some steric strain as the hydrogens of the CH2-CH2 bringe are close to the malic anhydride. The endo form deosn't sufffer this strain as much as the bridging portion is the double bond CH-CH section, so the hydrogens are further away.

In order to explore the secondary orbtial overlap, the molecular orbitals of the system were calculated using the AM1 semi-empirical method.

{| class="wikitable" border="1"

! !! Exo TS !! !! Endo TS !!
|-
| || HOMO || LUMO || HOMO || LUMO
|-
| ||[[Image:exo homo sp3609.jpeg|200px| ]] || [[Image:exo lumo sp3609.jpeg|200px| ]] ||[[Image:endo homo sp3609.jpeg|200px| ]] || [[Image:endo lumo sp3609.jpeg|200px| ]]
|-
|Energy /a.u|| -0.34113 || -0.04051 || -0.34321 || -0.03567
|}

The HOMO of the endo TS is lower in energy than that of the exo TS. In the endo conformer the p orbitals of the oxygen are in the same region as the π systems. This means that there is an opportunity for mixing, which lowers the energy of the HOMO, stabilising the system. In the exo form the p orbitals of the oxygen are seperated from the π system, so there is no chance of them interacting.

= References =
<references />

File:Boat higher opt out.out

2011-12-16T13:57:57Z

Sp3609:

File:1ST OPT.LOG

2011-12-16T13:57:56Z

Sp3609:

File:2ND OPT.LOG

2011-12-16T13:57:56Z

Sp3609:

File:2ND OPTIMISATION.LOG

2011-12-16T13:57:56Z

Sp3609:

File:QST2 OPT.LOG

2011-12-16T13:57:55Z

Sp3609:

Rep:Mod:sp33

2011-12-16T13:56:44Z

Sp3609: /* Chair Transition States */

= Cope Rearrangement =
The cope rearrangement was discovered by A. Cope and E. Hardy in 1939<ref>A.Cope et al, ''J. Am. Chem. Soc.'', 1940, 62, 441-444 {{DOI|10.1021/ja01859a055}}</ref>The reaction is a [3,3] sigmatropic reaction that has been proven to occur concertedly.<ref>O. Wiest, A.Kersey, et. al; ''J. Am. Chem. Soc.''; 1994, '''116''', 10336-10337{{DOI|10.1021/ja00101a078}}</ref>
[[Image:copeschemesp.gif|300px| ]]

It is generally accepted that the reaction goes via a chair or boat like transition state.

[[Image:TSsp.gif|300px| ]]

The low-energy minima and transition structures on the C6H10 potential energy surface can be found, in order to determine the preferred reaction mechanism.

== optimising the reactant and product ==

A molecule of 1,5 hexadiene (1) was drawn using gaussian with an anti linkage of the main chain. It was then optimised using the HF/3-21G method and then the energy and symmetry were recorded in the table below. A gauche conformer (2) of the molecule was also optimised and analysed. The gauche conformer was lower in energy . In order to calculate the activation energies and enthalpies the lowest energy conformer is needed. Because the Gauche conformer is lower in energy, it would make sense to try structures with more gauche conformations in them. Several structures were tried to see which was lowest in energy. They were then identified by comparing to the low energy conformers in [[Mod:phys3#Appendix 1|Appendix 1]] .

{| class="wikitable" border="1"

! !! conformer !!Energy /a.u !! Energy /Kcalmol-1 !! Point Group !! Conformation
|-
| 1 || [[Image:conformer 1sp.jpeg|thumb|100px|<jmolFile text="Conformer 1">confomer1sp.mol</jmolFile> ]] || -231.69097 || -145388.28 || C1 || anti 4
|-
| 2 || [[Image:conformer 2sp.jpeg|thumb|100px|<jmolFile text="Conformer 2">confomer2sp.mol</jmolFile> ]]|| -231.68962 || -145387.43 || C1 || gauche 5
|-
| 3 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Conformer 3">confomer3sp.mol</jmolFile> ]] || -231.69260 || -145389.30 || C2 || anti 1
|-
| 4 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Conformer 4">confomer4sp.mol</jmolFile> ]] || -231.69266 || -145389.34 || C1 || gauche 3
|-
| 5 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Conformer 5">confomer5sp.mol</jmolFile> ]] || -231.69254 || -145389.26 || Ci || anti 2

|}

The lowest energy conformation is the gauche 3 conformation followed by the anti 1 conformation. The introduction of the gauche linkage means the molecule is more stable as there are now more favorable van der Waahls interactions.
The lowest three conformations were then optimised at the B3LYP/6-31G* level, as this is a more powerful technique and gives more accurate energies.

{| class="wikitable" border="1"

! conformer !! Energy /a.u !! Energy /Kcalmol-1 || input structure || output structure
|-
| Gauche 3|| -234.61133 || -147220.83 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">confomer4sp.mol</jmolFile> ]] || [[Image:gauche3sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">gauche3sp.mol</jmolFile> ]]
|-
| Anti 1 || -234.61179 || -147221.12 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Anti 1">confomer3sp.mol</jmolFile> ]] || [[Image:anti1sp.jpeg|thumb|100px|<jmolFile text="Anti 1">anti1sp.mol</jmolFile> ]]
|-
| Anti 2 || -234.61171 || -147221.07 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Anti 2">confomer5sp.mol</jmolFile> ]] || [[Image:anti2sp.jpeg|thumb|100px|<jmolFile text="Anti 2">anti2sp.mol</jmolFile> ]]
|}
When calculated at this higher level the energies of the three conformers change and the anti 1 conformer is now the lowest in energy. As can be seen from the images there isn't a large difference between the structures from the two levels of optimisation.

When the reaction occurs it goes from the Ci symmetry conformer. Therefore the geometries from the two calculations can be compared directly.

{| class="wikitable" border="1"

! method !! Bond lengths/Å and Angles /°
|-
| HF/3-21G ||[[Image:cibondsp.jpeg|400px| ]]
|-
| B3LYP/6-31G* ||[[Image:ci2bondssp.jpeg|400px| ]]
|}
The bond lengths are very similar but the angles are relatively different. with the B3LYP structure being slightly more linear.

The frequency analysis of this conformer was performed to ensure that a true minima had been found.
[[Image:IR anti2sp.jpeg|thumb|center|400px| Ci conformer ]]
As can be seen in the spectra, there are no negative vibrations, so it is confirmed that an actual minima has been found as oppose to a transition atate maxima.

The various energies of the system are also calculated using this method. The sum of the electronic and zero point energies is the potential energy at 0K. The sum of electronic and thermal energies gives the energy at 298.15K and 1 atmosphere. It contains contributions from the translational, rotational and vibrational energies. The third gives the enthalpy and takes into a correction for room temperature as H = E + RT. The fourth is the energy with the entropic contribution to the free energy considered. The final three are calculated at 298.15K and all energies are given in atomic units.

{| class="wikitable" border="1"

! !! a.u. !! kJmol-1
|-
| Sum of electronic and zero point energies || -234.469204 || -615599
|-
| Sum of electronic and thermal energies || -234.461857 || -615580
|-
| Sum of electronic and thermal enthalpies || -234.460913 || -615577
|-
| Sum of electronic and thermal free energies || -234.500777 || -615682
|}

Calculation files: https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Gauche_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_confomer_2nd.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Gauche_3rd_confomer.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_confomer_2_ci.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_3rd.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:2nd_gauche_confomer.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_2_freq_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti2_2nd_opt_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_2_freq_out.out

== Optimising the Transition States ==
=== Chair Transition States ===

To begin with an allyl fragment was optimised at the HF/3-21G level. Two of these fragments were then combined to give an initial structure for the chair T.S. The two fragments were placed with the ends of the allyl fragments 2.2Å apart and then optimised using in two different ways.

The first method calculates the force constant matriix in order to find the position of the T.S. The structure was optimised and the frequency analysis in one step.[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S 1">chair ts opt 1.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932246
|-
| RMS Gradient Norm /a.u.|| 0.00001378
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -818.97 which corresponds to the formation of one bond and breaking of the other.

[[Image:chairvib1sp.jpeg|300px| ]]

The second method uses a frozen co-ordinate method. The two allyl fragments were optimised with the two ends frozen at 2.2Å at the HF/3-21G level and then again with then bonds unfrozen. [[Image:chair ts otheropt part 2.jpeg|thumb|300px|<jmolFile text="Chair T.S 2">chair ts opt 2.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932189
|-
| RMS Gradient Norm /a.u.|| 0.00005807

|}

The geometries of the two optimised transition states are compared in the table below

{| class="wikitable" border="1"

! !! 1st Method || 2nd Method
|-
| C-C bond formed/broken || 2.02 || 2.02
|-
| other C-C bonds || 1.389 || 1.389
|}

They both give identical transition state geometries so either can be used depending on how much information about the transition state is known.

Calculation Data:https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ICR_OF_CHAIR.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:ICR_CHAIR_2.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIT_TS_OTHER_OPT_PART_2.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIT_TS_OTHER_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIR_TS_GUESS_1_OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIR_ICR.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:CHAIR_B3OPT.LOG
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Chair_higher_opt_out.out

=== Boat Transition State ===
The Boat T.S was optimised using the QST2 method. This takes the reactant structure and product structure and extrapolates between the two, to find the transition state.The two structures were positioned so they are similar to a boat conformation and then optimised. [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat ts">QST2 opt.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60279992
|-
| RMS Gradient Norm /a.u.|| 0.00013432
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -840.35 which corresponds to the formation of one bond and breaking of the other.

[[Image:boat higher vib sp.jpeg|300px| ]]

The bonds that are being formed are 2.14Å and the other C-C bonds are 1.382Å.

=== Intrinsic reaction co-ordinate ===

From looking at the transition states, its near on impossible to tell which conformer the reaction path will lead to. However using the IRC method the minimum energy path to the nearest minima can be followed. Because the reaction is symmetric it only needs to be run in the forward reaction.

This was initially done with 50 points along the pathway, however that didn't lead to a minima, so it was run again with 100 points.

{| class="wikitable" border="1"

! Points along the IRC !! Energy Graph !! RMS gradient Graph || Inital Structure || Final Structure
|-
| 50 || [[Image:chair icr 1 energy graph.jpeg|200px| ]] || [[Image:chair icr 1 rms graph.jpeg|200px| ]] || [[Image:icr 1 initial.jpeg|200px| ]] || [[Image:icr 1 final.jpeg|200px| ]]
|-
| 100 || [[Image:ICR 2 chair energy graph.jpeg|300px| ]] || [[Image:ICR 2 chair rms graph.jpeg|300px| ]] || [[Image:icr 2 initial.jpeg|200px| ]] || [[Image:icr 2 final.jpeg|200px| ]]
|}

As can be seen the gradient doesn't reach zero, even for 100 points, and the final structure is almost identical. In order to get further the force constants may need to be calculated at every step instead of just once.

== Calculating Activation Energies ==

To calculate the activation energies of the reaction via each transition state the transition states need to be optimised at a higher level to give more accurate energies. Therefore both were optimised at the B3LYP/6-31G* level.

{| class="wikitable" border="1"
|+ Chair T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure ||[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S ">chair ts opt 1.mol</jmolFile> ]] || [[Image:chair higher opt.jpeg|thumb|300px|<jmolFile text="Chair T.S">chair higher opt.mol</jmolFile> ]]
|-
| Energy || -231.619322 || -234.55698
|-
| new c-c bond lengths /Å || 2.02 || 1.97
|-
| other bond length /Å || 1.38 || 1.41
|-
| Frequency of imaginary vibration || -818.97 || -565.54
|}
{| class="wikitable" border="1"
|+ Boat T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure || [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">QST2 opt.mol</jmolFile> ]] || [[Image:boat higher opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">boat higher opt sp.mol</jmolFile> ]]
|-
| Energy || -231.602799 || -234.54309
|-
| new c-c bond lengths /Å || 2.14 || 2.21
|-
| other bond length /Å || 1.38 || 1.39
|-
| Frequency of imaginary vibration || -840.35 || -530.36
|}

As can be seen, the geometries are relatively similar but the energies are very different.
A summary of the energies is given below:

{| class="wikitable" border="1"

! !! Electronic energy !! Sum of electronic and zero point energies !! Sum of electronic and thermal energies !! Sum of electronic and thermal enthalpies !! Sum of electronic and thermal free energies
|-
| Reactant || -234.611710 || -234.469204 || -234.461857 || -234.460913 || -234.500777
|-
| Chair T.S || -234.556983 || -234.414929 || -234.409008 || -234.408064 || -234.443814
|-
| Boat T.S || -234.543093 || -234.402342 || -234.396008 || -234.395063 ||-234.431752
|}

The Activation Energy of the reaction can be calculated by Eactivation = Etransition state - Ereactants

To calcultate the Activation Energy at rooom temperature 298.15 K then the sum of the electronic and thermal energies should be used. To calculate it at 0K then the sum of electronic and zero point energies should be used.

Chair Transition State
@ 298.15 KEactivation = -234.409008- -234.461857 = 0.052849 au = 33.16 kcalmol-1
@ 0 KEactivation = -234.414929- -234.469204 = 0.054275 au = 34.06 kcalmol-1
Boat Transition State
@ 298.15 KEactivation = -234.396008- -234.461857 = 0.065849 au = 41.32 kcalmol-1
@ 0 KEactivation = -234.402342- -234.469204 = 0.066862 au = 41.96 kcalmol-1

The reaction that goes via a Chair Transition State has a lower activion energy and is therefore the way the reaction proceeds.

The experimental values for the activation energy via a chair transition state is 33.5 kcalmol-1 and via the boat transition state 44.7 kcalmol-1. The calculated values are in very close agreement with the experimental values.

= Diels-Alder Cycloaddition =
The Diels Alder reaction is a [4+2] cycloaddition. The reaction was discovered in 1928 by Otto Diels and Kurt Alder.<ref>Diels, O. Alder, K.; ''Justus Liebig's Annalen der Chemie''; 1928; '''460'''; 98–122.{{DOI|10.1002/jlac.19284600106}}</ref>
The reaction can be very stereo and regio specific depending on the elctronics and sterics of the reactants used.

Two different reactions will be looked at below:
1) the reaction between Cis butadiene and Ethene. This is the simplest Diels-Alder reaction possible, there are no side groups to influence the reaction sterically or electronicly, so the basics interactions of the reaction can be clearly seen.
2) the reaction between Malic anhydride + 1,3 Cyclohexadiene. This is more complex, as both the steric effect of the briding section and the electronic effect of the functionalised dienophile must be considered.

==Cis Butadiene and ethene ==

[[Image:butadiene reaction scheme sp.gif|thumb|widthpx| ]]

Cis butadiene was optimised at the HF/3-21G level.
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FOPT
|-
| Calculation Method ||RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -154.05394317
|-
| RMS Gradient Norm /a.u.|| 0.00007352
|}

The HOMO and LUMO were then calculated using the AM1 semi-empirical MO method.[[Image:butadiene plane sp.gif|thumb|200px|Plane of symmetry ]]

{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:butadiene homo sp.jpeg|200px]] || [[Image:butadiene lumo sp.jpeg|200px]]
|-
| Energy /a.u.|| -0.35083 || 0.01977
|-
| Symmetry || a || s
|}

The symmetry of the orbitals are determined with respect to the plane which runs through the center of the middle bond .
If the orbital is symmetric with respect to reflection in the plane, then it is labeled s and if not it is labeled a.

The transition state for the reaction has an envelope-like structure. It was drawn in gaussview with the ends of the two fragments positioned 2.2Å apart. The transition structure was optimised using at the HF/3-21G level using the QST2 method.
[[Image:transition state sp.jpeg|thumb|200px|<jmolFile text="Butadiene + ethene T.S">TS sp3609.mol</jmolFile> ]]
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60320837
|-
| RMS Gradient Norm /a.u.|| 0.00002624
|-
| Imaginary frequencies || 1
|}

[[Image:transition state geometry sp.jpeg|200px| ]]

The various bond lengths and angels of the transition state are detailed above. Typical sp3 c-c bonds are ~1.54Å and sp2 c-c bonds are ~1.33Å. The Van der Waahls radius of carbon is 1.70Å<ref>A. Bondi; ''J. Phys. Chem.'', 1964, '''68 (3)''', pp441–451 {{DOI|10.1021/j100785a001}}</ref> The σ bonds that are long compared to a σ bond, but the bonds in the cis butadiene are all approximately equal. This suggests that the starting point of the change in structure is a change in the electronic structure rather than the formation of new bonds.

[[Image:transition vibration sp.jpeg|thumb|100px| ]]The imaginary frequency occurs at -818.34 and corresponds to the formation of two new bonds in a synchronous fashion. As the new bonds form, the double bonds lengthen and the single bond in the butadiene contracts, which corresponds to the geometric changes that occur in the reaction. The lowest positive frequency occurs at 116.73 and corresponds to an asychronus movement of the two ethene carons towards the butadiene ends.

In order to ensure that the transition state had been found the IRC method was used to find the minimum energy pathway to the local minima, which should be the product.
The initial structure looks like the starting material and then the final structure looks like the transition state.

[[Image:ICR butadiene energy graph sp.jpeg|400px| ]][[Image:ICR butadiene rms graph sp.jpeg|400pxpx| ]]

[[Image:ICR initial structure butadiene sp.jpeg|thumb|left|200px|Initial Structure| ]][[Image:ICR final structure butadiene sp.jpeg|thumb|center|200pxpx|Final Structure| ]]

The Molecular orbitals of the transition state were calculated using the AM1 semi-empirical method. The symmetry was determined with respect to the plane of symmetry detailed above.
{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:TS homo sp.jpeg|200px]] || [[Image:TS lumo sp.jpeg|200px]]
|-
| Energy /a.u. || -0.32593 || 0.01842
|-
| Symmetry ||a || s
|}

The HOMO of ethene is the пc-c orbital which has s symmetry and the LUMO is the п*c-c orbital, which has a symmetry. The orbitals of ethene and butadiene can only interact if they have the same symmetry label. Therefore it can be seen that the HOMO of the transition state is made of the HOMO of butadiene and the LUMO of ethene and therefore is antisymmetric. And the LUMO of the transition state is made of the LUMO of butadiene and the HOMO of ethene and is symmetric. The reaction is allowed because the HOMO/LUMO pairs interact and are of similar sizes, so there is significant overlap.

== Malic anhydride + 1,3 Cyclohexadiene ==

[[Image:reaction scheme sp.gif|200px| reaction between malic anhydride + 1,3 cyclohexadiene ]]
The reaction between malic anhydride + 1,3 cyclohexadiene forms mainly the endo product, the reaction is presumed to be kinetically controlled. This can be confirmed by comparing the energies of the transition states.

In order to find the transition states both reactants were optimised at the HF/3-12G level.
{| class="wikitable" border="1"
|+ Optimisation summary
! heading !! Maleic Anhydride || 1,3 Cyclohexadiene
|-
| || [[Image:MA sp.jpeg|thumb|200px|<jmolFile text="Maleic Anhydride">MA sp.mol</jmolFile> ]] ||[[Image:cyclo sp.jpeg|thumb|200px|<jmolFile text="1,3 Cyclohexadiene">cyclo sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -375.10351323 || -230.54323110
|-
| RMS Gradient Norm /a.u.|| 0.00012414 || 0.00004255
|}

The Exo and Endo transition states were optimised by calulating the hessian.
{| class="wikitable" border="1"
|+ Optimisation summary
! !! Exo TS || Endo TS
|-
| || [[Image:exo ts sp3609.jpeg|thumb|200px|<jmolFile text="Exo TS">exo opt sp.mol</jmolFile> ]] || [[Image:endo ts sp3609.jpeg|thumb|200px|<jmolFile text="Endo TS">endo opt sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -605.60359122 || -605.61036815
|-
| RMS Gradient Norm /a.u.|| 0.00001656 || 0.00003160
|}

As can be seen the Exo transition state is higher in energy and so as the endo product is the one that is formed then it can be presumed that the reaction is kinetically controlled. Kinetically controlled reactions go via the lowest energy transition state regardless of whether or not it leads to the lowest energy product. It is generally considered that the stability of the endo transition state is due to steric effects destabilising the exo form and secondary orbital overlap stabilising the endo form.

[[Image:exo ts vib sp.jpeg|left|thumb|200px| Exo TS ]][[Image:endo ts vib sp.jpeg|center|thumb|200px|Endo TS]]
The frequency analysis for both was calculated and the imaginary frequency for the exo t.s. occurs at -647.33 ant for the endo t.s it occurs at -643.57. For both the vibration correspond with the synchronous formation of two bonds between the fragments.

The geometries of the the two structures are given below:

{| class="wikitable" border="1"
| Exo || Endo
|-
| [[Image:exo ts geom sp.jpeg|400px| ]] ||[[Image:endo ts geom sp.jpeg|400px| ]]
|-
| [[Image:exo o geom sp.jpeg|400px| ]] ||[[Image:endo o geom sp.jpeg|400px| ]]
|}
As can be seen both of the geometries are very similar, all the bond lengths ae more or less the same, the only diffenece is the orientation of the two fragments. However in the exo form there may be more steric strain as the hydrogens for the cyclohexadiene are closer to the maleic anhydride. As can be seen in the second pictures the exo form suffers some steric strain as the hydrogens of the CH2-CH2 bringe are close to the malic anhydride. The endo form deosn't sufffer this strain as much as the bridging portion is the double bond CH-CH section, so the hydrogens are further away.

In order to explore the secondary orbtial overlap, the molecular orbitals of the system were calculated using the AM1 semi-empirical method.

{| class="wikitable" border="1"

! !! Exo TS !! !! Endo TS !!
|-
| || HOMO || LUMO || HOMO || LUMO
|-
| ||[[Image:exo homo sp3609.jpeg|200px| ]] || [[Image:exo lumo sp3609.jpeg|200px| ]] ||[[Image:endo homo sp3609.jpeg|200px| ]] || [[Image:endo lumo sp3609.jpeg|200px| ]]
|-
|Energy /a.u|| -0.34113 || -0.04051 || -0.34321 || -0.03567
|}

The HOMO of the endo TS is lower in energy than that of the exo TS. In the endo conformer the p orbitals of the oxygen are in the same region as the π systems. This means that there is an opportunity for mixing, which lowers the energy of the HOMO, stabilising the system. In the exo form the p orbitals of the oxygen are seperated from the π system, so there is no chance of them interacting.

= References =
<references />

File:Chair higher opt out.out

2011-12-16T13:55:17Z

Sp3609:

File:CHAIR B3OPT.LOG

2011-12-16T13:55:17Z

Sp3609:

File:CHAIR ICR.LOG

2011-12-16T13:55:16Z

Sp3609:

File:CHAIR TS GUESS 1 OPT.LOG

2011-12-16T13:55:16Z

Sp3609:

File:CHAIT TS OTHER OPT.LOG

2011-12-16T13:55:15Z

Sp3609:

File:CHAIT TS OTHER OPT PART 2.LOG

2011-12-16T13:55:15Z

Sp3609:

File:ICR CHAIR 2.LOG

2011-12-16T13:55:14Z

Sp3609:

File:ICR OF CHAIR.LOG

2011-12-16T13:55:13Z

Sp3609:

File:QST2 opt.mol

2011-12-16T13:53:17Z

Sp3609:

Rep:Mod:sp33

2011-12-16T13:52:14Z

Sp3609: /* optimising the reactant and product */

= Cope Rearrangement =
The cope rearrangement was discovered by A. Cope and E. Hardy in 1939<ref>A.Cope et al, ''J. Am. Chem. Soc.'', 1940, 62, 441-444 {{DOI|10.1021/ja01859a055}}</ref>The reaction is a [3,3] sigmatropic reaction that has been proven to occur concertedly.<ref>O. Wiest, A.Kersey, et. al; ''J. Am. Chem. Soc.''; 1994, '''116''', 10336-10337{{DOI|10.1021/ja00101a078}}</ref>
[[Image:copeschemesp.gif|300px| ]]

It is generally accepted that the reaction goes via a chair or boat like transition state.

[[Image:TSsp.gif|300px| ]]

The low-energy minima and transition structures on the C6H10 potential energy surface can be found, in order to determine the preferred reaction mechanism.

== optimising the reactant and product ==

A molecule of 1,5 hexadiene (1) was drawn using gaussian with an anti linkage of the main chain. It was then optimised using the HF/3-21G method and then the energy and symmetry were recorded in the table below. A gauche conformer (2) of the molecule was also optimised and analysed. The gauche conformer was lower in energy . In order to calculate the activation energies and enthalpies the lowest energy conformer is needed. Because the Gauche conformer is lower in energy, it would make sense to try structures with more gauche conformations in them. Several structures were tried to see which was lowest in energy. They were then identified by comparing to the low energy conformers in [[Mod:phys3#Appendix 1|Appendix 1]] .

{| class="wikitable" border="1"

! !! conformer !!Energy /a.u !! Energy /Kcalmol-1 !! Point Group !! Conformation
|-
| 1 || [[Image:conformer 1sp.jpeg|thumb|100px|<jmolFile text="Conformer 1">confomer1sp.mol</jmolFile> ]] || -231.69097 || -145388.28 || C1 || anti 4
|-
| 2 || [[Image:conformer 2sp.jpeg|thumb|100px|<jmolFile text="Conformer 2">confomer2sp.mol</jmolFile> ]]|| -231.68962 || -145387.43 || C1 || gauche 5
|-
| 3 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Conformer 3">confomer3sp.mol</jmolFile> ]] || -231.69260 || -145389.30 || C2 || anti 1
|-
| 4 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Conformer 4">confomer4sp.mol</jmolFile> ]] || -231.69266 || -145389.34 || C1 || gauche 3
|-
| 5 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Conformer 5">confomer5sp.mol</jmolFile> ]] || -231.69254 || -145389.26 || Ci || anti 2

|}

The lowest energy conformation is the gauche 3 conformation followed by the anti 1 conformation. The introduction of the gauche linkage means the molecule is more stable as there are now more favorable van der Waahls interactions.
The lowest three conformations were then optimised at the B3LYP/6-31G* level, as this is a more powerful technique and gives more accurate energies.

{| class="wikitable" border="1"

! conformer !! Energy /a.u !! Energy /Kcalmol-1 || input structure || output structure
|-
| Gauche 3|| -234.61133 || -147220.83 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">confomer4sp.mol</jmolFile> ]] || [[Image:gauche3sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">gauche3sp.mol</jmolFile> ]]
|-
| Anti 1 || -234.61179 || -147221.12 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Anti 1">confomer3sp.mol</jmolFile> ]] || [[Image:anti1sp.jpeg|thumb|100px|<jmolFile text="Anti 1">anti1sp.mol</jmolFile> ]]
|-
| Anti 2 || -234.61171 || -147221.07 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Anti 2">confomer5sp.mol</jmolFile> ]] || [[Image:anti2sp.jpeg|thumb|100px|<jmolFile text="Anti 2">anti2sp.mol</jmolFile> ]]
|}
When calculated at this higher level the energies of the three conformers change and the anti 1 conformer is now the lowest in energy. As can be seen from the images there isn't a large difference between the structures from the two levels of optimisation.

When the reaction occurs it goes from the Ci symmetry conformer. Therefore the geometries from the two calculations can be compared directly.

{| class="wikitable" border="1"

! method !! Bond lengths/Å and Angles /°
|-
| HF/3-21G ||[[Image:cibondsp.jpeg|400px| ]]
|-
| B3LYP/6-31G* ||[[Image:ci2bondssp.jpeg|400px| ]]
|}
The bond lengths are very similar but the angles are relatively different. with the B3LYP structure being slightly more linear.

The frequency analysis of this conformer was performed to ensure that a true minima had been found.
[[Image:IR anti2sp.jpeg|thumb|center|400px| Ci conformer ]]
As can be seen in the spectra, there are no negative vibrations, so it is confirmed that an actual minima has been found as oppose to a transition atate maxima.

The various energies of the system are also calculated using this method. The sum of the electronic and zero point energies is the potential energy at 0K. The sum of electronic and thermal energies gives the energy at 298.15K and 1 atmosphere. It contains contributions from the translational, rotational and vibrational energies. The third gives the enthalpy and takes into a correction for room temperature as H = E + RT. The fourth is the energy with the entropic contribution to the free energy considered. The final three are calculated at 298.15K and all energies are given in atomic units.

{| class="wikitable" border="1"

! !! a.u. !! kJmol-1
|-
| Sum of electronic and zero point energies || -234.469204 || -615599
|-
| Sum of electronic and thermal energies || -234.461857 || -615580
|-
| Sum of electronic and thermal enthalpies || -234.460913 || -615577
|-
| Sum of electronic and thermal free energies || -234.500777 || -615682
|}

Calculation files: https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Gauche_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_confomer_2nd.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Gauche_3rd_confomer.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_confomer_2_ci.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_3rd.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:2nd_gauche_confomer.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_2_freq_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti2_2nd_opt_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_2_freq_out.out

== Optimising the Transition States ==
=== Chair Transition States ===

To begin with an allyl fragment was optimised at the HF/3-21G level. Two of these fragments were then combined to give an initial structure for the chair T.S. The two fragments were placed with the ends of the allyl fragments 2.2Å apart and then optimised using in two different ways.

The first method calculates the force constant matriix in order to find the position of the T.S. The structure was optimised and the frequency analysis in one step.[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S 1">chair ts opt 1.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932246
|-
| RMS Gradient Norm /a.u.|| 0.00001378
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -818.97 which corresponds to the formation of one bond and breaking of the other.

[[Image:chairvib1sp.jpeg|300px| ]]

The second method uses a frozen co-ordinate method. The two allyl fragments were optimised with the two ends frozen at 2.2Å at the HF/3-21G level and then again with then bonds unfrozen. [[Image:chair ts otheropt part 2.jpeg|thumb|300px|<jmolFile text="Chair T.S 2">chair ts opt 2.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932189
|-
| RMS Gradient Norm /a.u.|| 0.00005807

|}

The geometries of the two optimised transition states are compared in the table below

{| class="wikitable" border="1"

! !! 1st Method || 2nd Method
|-
| C-C bond formed/broken || 2.02 || 2.02
|-
| other C-C bonds || 1.389 || 1.389
|}

They both give identical transition state geometries so either can be used depending on how much information about the transition state is known.

=== Boat Transition State ===
The Boat T.S was optimised using the QST2 method. This takes the reactant structure and product structure and extrapolates between the two, to find the transition state.The two structures were positioned so they are similar to a boat conformation and then optimised. [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat ts">QST2 opt.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60279992
|-
| RMS Gradient Norm /a.u.|| 0.00013432
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -840.35 which corresponds to the formation of one bond and breaking of the other.

[[Image:boat higher vib sp.jpeg|300px| ]]

The bonds that are being formed are 2.14Å and the other C-C bonds are 1.382Å.

=== Intrinsic reaction co-ordinate ===

From looking at the transition states, its near on impossible to tell which conformer the reaction path will lead to. However using the IRC method the minimum energy path to the nearest minima can be followed. Because the reaction is symmetric it only needs to be run in the forward reaction.

This was initially done with 50 points along the pathway, however that didn't lead to a minima, so it was run again with 100 points.

{| class="wikitable" border="1"

! Points along the IRC !! Energy Graph !! RMS gradient Graph || Inital Structure || Final Structure
|-
| 50 || [[Image:chair icr 1 energy graph.jpeg|200px| ]] || [[Image:chair icr 1 rms graph.jpeg|200px| ]] || [[Image:icr 1 initial.jpeg|200px| ]] || [[Image:icr 1 final.jpeg|200px| ]]
|-
| 100 || [[Image:ICR 2 chair energy graph.jpeg|300px| ]] || [[Image:ICR 2 chair rms graph.jpeg|300px| ]] || [[Image:icr 2 initial.jpeg|200px| ]] || [[Image:icr 2 final.jpeg|200px| ]]
|}

As can be seen the gradient doesn't reach zero, even for 100 points, and the final structure is almost identical. In order to get further the force constants may need to be calculated at every step instead of just once.

== Calculating Activation Energies ==

To calculate the activation energies of the reaction via each transition state the transition states need to be optimised at a higher level to give more accurate energies. Therefore both were optimised at the B3LYP/6-31G* level.

{| class="wikitable" border="1"
|+ Chair T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure ||[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S ">chair ts opt 1.mol</jmolFile> ]] || [[Image:chair higher opt.jpeg|thumb|300px|<jmolFile text="Chair T.S">chair higher opt.mol</jmolFile> ]]
|-
| Energy || -231.619322 || -234.55698
|-
| new c-c bond lengths /Å || 2.02 || 1.97
|-
| other bond length /Å || 1.38 || 1.41
|-
| Frequency of imaginary vibration || -818.97 || -565.54
|}
{| class="wikitable" border="1"
|+ Boat T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure || [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">QST2 opt.mol</jmolFile> ]] || [[Image:boat higher opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">boat higher opt sp.mol</jmolFile> ]]
|-
| Energy || -231.602799 || -234.54309
|-
| new c-c bond lengths /Å || 2.14 || 2.21
|-
| other bond length /Å || 1.38 || 1.39
|-
| Frequency of imaginary vibration || -840.35 || -530.36
|}

As can be seen, the geometries are relatively similar but the energies are very different.
A summary of the energies is given below:

{| class="wikitable" border="1"

! !! Electronic energy !! Sum of electronic and zero point energies !! Sum of electronic and thermal energies !! Sum of electronic and thermal enthalpies !! Sum of electronic and thermal free energies
|-
| Reactant || -234.611710 || -234.469204 || -234.461857 || -234.460913 || -234.500777
|-
| Chair T.S || -234.556983 || -234.414929 || -234.409008 || -234.408064 || -234.443814
|-
| Boat T.S || -234.543093 || -234.402342 || -234.396008 || -234.395063 ||-234.431752
|}

The Activation Energy of the reaction can be calculated by Eactivation = Etransition state - Ereactants

To calcultate the Activation Energy at rooom temperature 298.15 K then the sum of the electronic and thermal energies should be used. To calculate it at 0K then the sum of electronic and zero point energies should be used.

Chair Transition State
@ 298.15 KEactivation = -234.409008- -234.461857 = 0.052849 au = 33.16 kcalmol-1
@ 0 KEactivation = -234.414929- -234.469204 = 0.054275 au = 34.06 kcalmol-1
Boat Transition State
@ 298.15 KEactivation = -234.396008- -234.461857 = 0.065849 au = 41.32 kcalmol-1
@ 0 KEactivation = -234.402342- -234.469204 = 0.066862 au = 41.96 kcalmol-1

The reaction that goes via a Chair Transition State has a lower activion energy and is therefore the way the reaction proceeds.

The experimental values for the activation energy via a chair transition state is 33.5 kcalmol-1 and via the boat transition state 44.7 kcalmol-1. The calculated values are in very close agreement with the experimental values.

= Diels-Alder Cycloaddition =
The Diels Alder reaction is a [4+2] cycloaddition. The reaction was discovered in 1928 by Otto Diels and Kurt Alder.<ref>Diels, O. Alder, K.; ''Justus Liebig's Annalen der Chemie''; 1928; '''460'''; 98–122.{{DOI|10.1002/jlac.19284600106}}</ref>
The reaction can be very stereo and regio specific depending on the elctronics and sterics of the reactants used.

Two different reactions will be looked at below:
1) the reaction between Cis butadiene and Ethene. This is the simplest Diels-Alder reaction possible, there are no side groups to influence the reaction sterically or electronicly, so the basics interactions of the reaction can be clearly seen.
2) the reaction between Malic anhydride + 1,3 Cyclohexadiene. This is more complex, as both the steric effect of the briding section and the electronic effect of the functionalised dienophile must be considered.

==Cis Butadiene and ethene ==

[[Image:butadiene reaction scheme sp.gif|thumb|widthpx| ]]

Cis butadiene was optimised at the HF/3-21G level.
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FOPT
|-
| Calculation Method ||RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -154.05394317
|-
| RMS Gradient Norm /a.u.|| 0.00007352
|}

The HOMO and LUMO were then calculated using the AM1 semi-empirical MO method.[[Image:butadiene plane sp.gif|thumb|200px|Plane of symmetry ]]

{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:butadiene homo sp.jpeg|200px]] || [[Image:butadiene lumo sp.jpeg|200px]]
|-
| Energy /a.u.|| -0.35083 || 0.01977
|-
| Symmetry || a || s
|}

The symmetry of the orbitals are determined with respect to the plane which runs through the center of the middle bond .
If the orbital is symmetric with respect to reflection in the plane, then it is labeled s and if not it is labeled a.

The transition state for the reaction has an envelope-like structure. It was drawn in gaussview with the ends of the two fragments positioned 2.2Å apart. The transition structure was optimised using at the HF/3-21G level using the QST2 method.
[[Image:transition state sp.jpeg|thumb|200px|<jmolFile text="Butadiene + ethene T.S">TS sp3609.mol</jmolFile> ]]
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60320837
|-
| RMS Gradient Norm /a.u.|| 0.00002624
|-
| Imaginary frequencies || 1
|}

[[Image:transition state geometry sp.jpeg|200px| ]]

The various bond lengths and angels of the transition state are detailed above. Typical sp3 c-c bonds are ~1.54Å and sp2 c-c bonds are ~1.33Å. The Van der Waahls radius of carbon is 1.70Å<ref>A. Bondi; ''J. Phys. Chem.'', 1964, '''68 (3)''', pp441–451 {{DOI|10.1021/j100785a001}}</ref> The σ bonds that are long compared to a σ bond, but the bonds in the cis butadiene are all approximately equal. This suggests that the starting point of the change in structure is a change in the electronic structure rather than the formation of new bonds.

[[Image:transition vibration sp.jpeg|thumb|100px| ]]The imaginary frequency occurs at -818.34 and corresponds to the formation of two new bonds in a synchronous fashion. As the new bonds form, the double bonds lengthen and the single bond in the butadiene contracts, which corresponds to the geometric changes that occur in the reaction. The lowest positive frequency occurs at 116.73 and corresponds to an asychronus movement of the two ethene carons towards the butadiene ends.

In order to ensure that the transition state had been found the IRC method was used to find the minimum energy pathway to the local minima, which should be the product.
The initial structure looks like the starting material and then the final structure looks like the transition state.

[[Image:ICR butadiene energy graph sp.jpeg|400px| ]][[Image:ICR butadiene rms graph sp.jpeg|400pxpx| ]]

[[Image:ICR initial structure butadiene sp.jpeg|thumb|left|200px|Initial Structure| ]][[Image:ICR final structure butadiene sp.jpeg|thumb|center|200pxpx|Final Structure| ]]

The Molecular orbitals of the transition state were calculated using the AM1 semi-empirical method. The symmetry was determined with respect to the plane of symmetry detailed above.
{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:TS homo sp.jpeg|200px]] || [[Image:TS lumo sp.jpeg|200px]]
|-
| Energy /a.u. || -0.32593 || 0.01842
|-
| Symmetry ||a || s
|}

The HOMO of ethene is the пc-c orbital which has s symmetry and the LUMO is the п*c-c orbital, which has a symmetry. The orbitals of ethene and butadiene can only interact if they have the same symmetry label. Therefore it can be seen that the HOMO of the transition state is made of the HOMO of butadiene and the LUMO of ethene and therefore is antisymmetric. And the LUMO of the transition state is made of the LUMO of butadiene and the HOMO of ethene and is symmetric. The reaction is allowed because the HOMO/LUMO pairs interact and are of similar sizes, so there is significant overlap.

== Malic anhydride + 1,3 Cyclohexadiene ==

[[Image:reaction scheme sp.gif|200px| reaction between malic anhydride + 1,3 cyclohexadiene ]]
The reaction between malic anhydride + 1,3 cyclohexadiene forms mainly the endo product, the reaction is presumed to be kinetically controlled. This can be confirmed by comparing the energies of the transition states.

In order to find the transition states both reactants were optimised at the HF/3-12G level.
{| class="wikitable" border="1"
|+ Optimisation summary
! heading !! Maleic Anhydride || 1,3 Cyclohexadiene
|-
| || [[Image:MA sp.jpeg|thumb|200px|<jmolFile text="Maleic Anhydride">MA sp.mol</jmolFile> ]] ||[[Image:cyclo sp.jpeg|thumb|200px|<jmolFile text="1,3 Cyclohexadiene">cyclo sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -375.10351323 || -230.54323110
|-
| RMS Gradient Norm /a.u.|| 0.00012414 || 0.00004255
|}

The Exo and Endo transition states were optimised by calulating the hessian.
{| class="wikitable" border="1"
|+ Optimisation summary
! !! Exo TS || Endo TS
|-
| || [[Image:exo ts sp3609.jpeg|thumb|200px|<jmolFile text="Exo TS">exo opt sp.mol</jmolFile> ]] || [[Image:endo ts sp3609.jpeg|thumb|200px|<jmolFile text="Endo TS">endo opt sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -605.60359122 || -605.61036815
|-
| RMS Gradient Norm /a.u.|| 0.00001656 || 0.00003160
|}

As can be seen the Exo transition state is higher in energy and so as the endo product is the one that is formed then it can be presumed that the reaction is kinetically controlled. Kinetically controlled reactions go via the lowest energy transition state regardless of whether or not it leads to the lowest energy product. It is generally considered that the stability of the endo transition state is due to steric effects destabilising the exo form and secondary orbital overlap stabilising the endo form.

[[Image:exo ts vib sp.jpeg|left|thumb|200px| Exo TS ]][[Image:endo ts vib sp.jpeg|center|thumb|200px|Endo TS]]
The frequency analysis for both was calculated and the imaginary frequency for the exo t.s. occurs at -647.33 ant for the endo t.s it occurs at -643.57. For both the vibration correspond with the synchronous formation of two bonds between the fragments.

The geometries of the the two structures are given below:

{| class="wikitable" border="1"
| Exo || Endo
|-
| [[Image:exo ts geom sp.jpeg|400px| ]] ||[[Image:endo ts geom sp.jpeg|400px| ]]
|-
| [[Image:exo o geom sp.jpeg|400px| ]] ||[[Image:endo o geom sp.jpeg|400px| ]]
|}
As can be seen both of the geometries are very similar, all the bond lengths ae more or less the same, the only diffenece is the orientation of the two fragments. However in the exo form there may be more steric strain as the hydrogens for the cyclohexadiene are closer to the maleic anhydride. As can be seen in the second pictures the exo form suffers some steric strain as the hydrogens of the CH2-CH2 bringe are close to the malic anhydride. The endo form deosn't sufffer this strain as much as the bridging portion is the double bond CH-CH section, so the hydrogens are further away.

In order to explore the secondary orbtial overlap, the molecular orbitals of the system were calculated using the AM1 semi-empirical method.

{| class="wikitable" border="1"

! !! Exo TS !! !! Endo TS !!
|-
| || HOMO || LUMO || HOMO || LUMO
|-
| ||[[Image:exo homo sp3609.jpeg|200px| ]] || [[Image:exo lumo sp3609.jpeg|200px| ]] ||[[Image:endo homo sp3609.jpeg|200px| ]] || [[Image:endo lumo sp3609.jpeg|200px| ]]
|-
|Energy /a.u|| -0.34113 || -0.04051 || -0.34321 || -0.03567
|}

The HOMO of the endo TS is lower in energy than that of the exo TS. In the endo conformer the p orbitals of the oxygen are in the same region as the π systems. This means that there is an opportunity for mixing, which lowers the energy of the HOMO, stabilising the system. In the exo form the p orbitals of the oxygen are seperated from the π system, so there is no chance of them interacting.

= References =
<references />

Rep:Mod:sp33

2011-12-16T13:51:02Z

Sp3609: /* optimising the reactant and product */

= Cope Rearrangement =
The cope rearrangement was discovered by A. Cope and E. Hardy in 1939<ref>A.Cope et al, ''J. Am. Chem. Soc.'', 1940, 62, 441-444 {{DOI|10.1021/ja01859a055}}</ref>The reaction is a [3,3] sigmatropic reaction that has been proven to occur concertedly.<ref>O. Wiest, A.Kersey, et. al; ''J. Am. Chem. Soc.''; 1994, '''116''', 10336-10337{{DOI|10.1021/ja00101a078}}</ref>
[[Image:copeschemesp.gif|300px| ]]

It is generally accepted that the reaction goes via a chair or boat like transition state.

[[Image:TSsp.gif|300px| ]]

The low-energy minima and transition structures on the C6H10 potential energy surface can be found, in order to determine the preferred reaction mechanism.

== optimising the reactant and product ==

A molecule of 1,5 hexadiene (1) was drawn using gaussian with an anti linkage of the main chain. It was then optimised using the HF/3-21G method and then the energy and symmetry were recorded in the table below. A gauche conformer (2) of the molecule was also optimised and analysed. The gauche conformer was lower in energy . In order to calculate the activation energies and enthalpies the lowest energy conformer is needed. Because the Gauche conformer is lower in energy, it would make sense to try structures with more gauche conformations in them. Several structures were tried to see which was lowest in energy. They were then identified by comparing to the low energy conformers in [[Mod:phys3#Appendix 1|Appendix 1]] .

{| class="wikitable" border="1"

! !! conformer !!Energy /a.u !! Energy /Kcalmol-1 !! Point Group !! Conformation
|-
| 1 || [[Image:conformer 1sp.jpeg|thumb|100px|<jmolFile text="Conformer 1">confomer1sp.mol</jmolFile> ]] || -231.69097 || -145388.28 || C1 || anti 4
|-
| 2 || [[Image:conformer 2sp.jpeg|thumb|100px|<jmolFile text="Conformer 2">confomer2sp.mol</jmolFile> ]]|| -231.68962 || -145387.43 || C1 || gauche 5
|-
| 3 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Conformer 3">confomer3sp.mol</jmolFile> ]] || -231.69260 || -145389.30 || C2 || anti 1
|-
| 4 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Conformer 4">confomer4sp.mol</jmolFile> ]] || -231.69266 || -145389.34 || C1 || gauche 3
|-
| 5 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Conformer 5">confomer5sp.mol</jmolFile> ]] || -231.69254 || -145389.26 || Ci || anti 2

|}

The lowest energy conformation is the gauche 3 conformation followed by the anti 1 conformation. The introduction of the gauche linkage means the molecule is more stable as there are now more favorable van der Waahls interactions.
The lowest three conformations were then optimised at the B3LYP/6-31G* level, as this is a more powerful technique and gives more accurate energies.

{| class="wikitable" border="1"

! conformer !! Energy /a.u !! Energy /Kcalmol-1 || input structure || output structure
|-
| Gauche 3|| -234.61133 || -147220.83 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">confomer4sp.mol</jmolFile> ]] || [[Image:gauche3sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">gauche3sp.mol</jmolFile> ]]
|-
| Anti 1 || -234.61179 || -147221.12 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Anti 1">confomer3sp.mol</jmolFile> ]] || [[Image:anti1sp.jpeg|thumb|100px|<jmolFile text="Anti 1">anti1sp.mol</jmolFile> ]]
|-
| Anti 2 || -234.61171 || -147221.07 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Anti 2">confomer5sp.mol</jmolFile> ]] || [[Image:anti2sp.jpeg|thumb|100px|<jmolFile text="Anti 2">anti2sp.mol</jmolFile> ]]
|}
When calculated at this higher level the energies of the three conformers change and the anti 1 conformer is now the lowest in energy. As can be seen from the images there isn't a large difference between the structures from the two levels of optimisation.

When the reaction occurs it goes from the Ci symmetry conformer. Therefore the geometries from the two calculations can be compared directly.

{| class="wikitable" border="1"

! method !! Bond lengths/Å and Angles /°
|-
| HF/3-21G ||[[Image:cibondsp.jpeg|400px| ]]
|-
| B3LYP/6-31G* ||[[Image:ci2bondssp.jpeg|400px| ]]
|}
The bond lengths are very similar but the angles are relatively different. with the B3LYP structure being slightly more linear.

The frequency analysis of this conformer was performed to ensure that a true minima had been found.
[[Image:IR anti2sp.jpeg|thumb|center|400px| Ci conformer ]]
As can be seen in the spectra, there are no negative vibrations, so it is confirmed that an actual minima has been found as oppose to a transition atate maxima.

The various energies of the system are also calculated using this method. The sum of the electronic and zero point energies is the potential energy at 0K. The sum of electronic and thermal energies gives the energy at 298.15K and 1 atmosphere. It contains contributions from the translational, rotational and vibrational energies. The third gives the enthalpy and takes into a correction for room temperature as H = E + RT. The fourth is the energy with the entropic contribution to the free energy considered. The final three are calculated at 298.15K and all energies are given in atomic units.

{| class="wikitable" border="1"

! !! a.u. !! kJmol-1
|-
| Sum of electronic and zero point energies || -234.469204 || -615599
|-
| Sum of electronic and thermal energies || -234.461857 || -615580
|-
| Sum of electronic and thermal enthalpies || -234.460913 || -615577
|-
| Sum of electronic and thermal free energies || -234.500777 || -615682
|}

Calculation files: https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Gauche_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti confomer 2nd.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Gauche 3rd confomer.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti confomer 2 ci.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti 3rd.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:2nd gauche confomer.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti 2 freq out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti2_2nd_opt_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_2_freq_out.out

== Optimising the Transition States ==
=== Chair Transition States ===

To begin with an allyl fragment was optimised at the HF/3-21G level. Two of these fragments were then combined to give an initial structure for the chair T.S. The two fragments were placed with the ends of the allyl fragments 2.2Å apart and then optimised using in two different ways.

The first method calculates the force constant matriix in order to find the position of the T.S. The structure was optimised and the frequency analysis in one step.[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S 1">chair ts opt 1.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932246
|-
| RMS Gradient Norm /a.u.|| 0.00001378
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -818.97 which corresponds to the formation of one bond and breaking of the other.

[[Image:chairvib1sp.jpeg|300px| ]]

The second method uses a frozen co-ordinate method. The two allyl fragments were optimised with the two ends frozen at 2.2Å at the HF/3-21G level and then again with then bonds unfrozen. [[Image:chair ts otheropt part 2.jpeg|thumb|300px|<jmolFile text="Chair T.S 2">chair ts opt 2.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932189
|-
| RMS Gradient Norm /a.u.|| 0.00005807

|}

The geometries of the two optimised transition states are compared in the table below

{| class="wikitable" border="1"

! !! 1st Method || 2nd Method
|-
| C-C bond formed/broken || 2.02 || 2.02
|-
| other C-C bonds || 1.389 || 1.389
|}

They both give identical transition state geometries so either can be used depending on how much information about the transition state is known.

=== Boat Transition State ===
The Boat T.S was optimised using the QST2 method. This takes the reactant structure and product structure and extrapolates between the two, to find the transition state.The two structures were positioned so they are similar to a boat conformation and then optimised. [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat ts">QST2 opt.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60279992
|-
| RMS Gradient Norm /a.u.|| 0.00013432
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -840.35 which corresponds to the formation of one bond and breaking of the other.

[[Image:boat higher vib sp.jpeg|300px| ]]

The bonds that are being formed are 2.14Å and the other C-C bonds are 1.382Å.

=== Intrinsic reaction co-ordinate ===

From looking at the transition states, its near on impossible to tell which conformer the reaction path will lead to. However using the IRC method the minimum energy path to the nearest minima can be followed. Because the reaction is symmetric it only needs to be run in the forward reaction.

This was initially done with 50 points along the pathway, however that didn't lead to a minima, so it was run again with 100 points.

{| class="wikitable" border="1"

! Points along the IRC !! Energy Graph !! RMS gradient Graph || Inital Structure || Final Structure
|-
| 50 || [[Image:chair icr 1 energy graph.jpeg|200px| ]] || [[Image:chair icr 1 rms graph.jpeg|200px| ]] || [[Image:icr 1 initial.jpeg|200px| ]] || [[Image:icr 1 final.jpeg|200px| ]]
|-
| 100 || [[Image:ICR 2 chair energy graph.jpeg|300px| ]] || [[Image:ICR 2 chair rms graph.jpeg|300px| ]] || [[Image:icr 2 initial.jpeg|200px| ]] || [[Image:icr 2 final.jpeg|200px| ]]
|}

As can be seen the gradient doesn't reach zero, even for 100 points, and the final structure is almost identical. In order to get further the force constants may need to be calculated at every step instead of just once.

== Calculating Activation Energies ==

To calculate the activation energies of the reaction via each transition state the transition states need to be optimised at a higher level to give more accurate energies. Therefore both were optimised at the B3LYP/6-31G* level.

{| class="wikitable" border="1"
|+ Chair T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure ||[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S ">chair ts opt 1.mol</jmolFile> ]] || [[Image:chair higher opt.jpeg|thumb|300px|<jmolFile text="Chair T.S">chair higher opt.mol</jmolFile> ]]
|-
| Energy || -231.619322 || -234.55698
|-
| new c-c bond lengths /Å || 2.02 || 1.97
|-
| other bond length /Å || 1.38 || 1.41
|-
| Frequency of imaginary vibration || -818.97 || -565.54
|}
{| class="wikitable" border="1"
|+ Boat T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure || [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">QST2 opt.mol</jmolFile> ]] || [[Image:boat higher opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">boat higher opt sp.mol</jmolFile> ]]
|-
| Energy || -231.602799 || -234.54309
|-
| new c-c bond lengths /Å || 2.14 || 2.21
|-
| other bond length /Å || 1.38 || 1.39
|-
| Frequency of imaginary vibration || -840.35 || -530.36
|}

As can be seen, the geometries are relatively similar but the energies are very different.
A summary of the energies is given below:

{| class="wikitable" border="1"

! !! Electronic energy !! Sum of electronic and zero point energies !! Sum of electronic and thermal energies !! Sum of electronic and thermal enthalpies !! Sum of electronic and thermal free energies
|-
| Reactant || -234.611710 || -234.469204 || -234.461857 || -234.460913 || -234.500777
|-
| Chair T.S || -234.556983 || -234.414929 || -234.409008 || -234.408064 || -234.443814
|-
| Boat T.S || -234.543093 || -234.402342 || -234.396008 || -234.395063 ||-234.431752
|}

The Activation Energy of the reaction can be calculated by Eactivation = Etransition state - Ereactants

To calcultate the Activation Energy at rooom temperature 298.15 K then the sum of the electronic and thermal energies should be used. To calculate it at 0K then the sum of electronic and zero point energies should be used.

Chair Transition State
@ 298.15 KEactivation = -234.409008- -234.461857 = 0.052849 au = 33.16 kcalmol-1
@ 0 KEactivation = -234.414929- -234.469204 = 0.054275 au = 34.06 kcalmol-1
Boat Transition State
@ 298.15 KEactivation = -234.396008- -234.461857 = 0.065849 au = 41.32 kcalmol-1
@ 0 KEactivation = -234.402342- -234.469204 = 0.066862 au = 41.96 kcalmol-1

The reaction that goes via a Chair Transition State has a lower activion energy and is therefore the way the reaction proceeds.

The experimental values for the activation energy via a chair transition state is 33.5 kcalmol-1 and via the boat transition state 44.7 kcalmol-1. The calculated values are in very close agreement with the experimental values.

= Diels-Alder Cycloaddition =
The Diels Alder reaction is a [4+2] cycloaddition. The reaction was discovered in 1928 by Otto Diels and Kurt Alder.<ref>Diels, O. Alder, K.; ''Justus Liebig's Annalen der Chemie''; 1928; '''460'''; 98–122.{{DOI|10.1002/jlac.19284600106}}</ref>
The reaction can be very stereo and regio specific depending on the elctronics and sterics of the reactants used.

Two different reactions will be looked at below:
1) the reaction between Cis butadiene and Ethene. This is the simplest Diels-Alder reaction possible, there are no side groups to influence the reaction sterically or electronicly, so the basics interactions of the reaction can be clearly seen.
2) the reaction between Malic anhydride + 1,3 Cyclohexadiene. This is more complex, as both the steric effect of the briding section and the electronic effect of the functionalised dienophile must be considered.

==Cis Butadiene and ethene ==

[[Image:butadiene reaction scheme sp.gif|thumb|widthpx| ]]

Cis butadiene was optimised at the HF/3-21G level.
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FOPT
|-
| Calculation Method ||RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -154.05394317
|-
| RMS Gradient Norm /a.u.|| 0.00007352
|}

The HOMO and LUMO were then calculated using the AM1 semi-empirical MO method.[[Image:butadiene plane sp.gif|thumb|200px|Plane of symmetry ]]

{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:butadiene homo sp.jpeg|200px]] || [[Image:butadiene lumo sp.jpeg|200px]]
|-
| Energy /a.u.|| -0.35083 || 0.01977
|-
| Symmetry || a || s
|}

The symmetry of the orbitals are determined with respect to the plane which runs through the center of the middle bond .
If the orbital is symmetric with respect to reflection in the plane, then it is labeled s and if not it is labeled a.

The transition state for the reaction has an envelope-like structure. It was drawn in gaussview with the ends of the two fragments positioned 2.2Å apart. The transition structure was optimised using at the HF/3-21G level using the QST2 method.
[[Image:transition state sp.jpeg|thumb|200px|<jmolFile text="Butadiene + ethene T.S">TS sp3609.mol</jmolFile> ]]
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60320837
|-
| RMS Gradient Norm /a.u.|| 0.00002624
|-
| Imaginary frequencies || 1
|}

[[Image:transition state geometry sp.jpeg|200px| ]]

The various bond lengths and angels of the transition state are detailed above. Typical sp3 c-c bonds are ~1.54Å and sp2 c-c bonds are ~1.33Å. The Van der Waahls radius of carbon is 1.70Å<ref>A. Bondi; ''J. Phys. Chem.'', 1964, '''68 (3)''', pp441–451 {{DOI|10.1021/j100785a001}}</ref> The σ bonds that are long compared to a σ bond, but the bonds in the cis butadiene are all approximately equal. This suggests that the starting point of the change in structure is a change in the electronic structure rather than the formation of new bonds.

[[Image:transition vibration sp.jpeg|thumb|100px| ]]The imaginary frequency occurs at -818.34 and corresponds to the formation of two new bonds in a synchronous fashion. As the new bonds form, the double bonds lengthen and the single bond in the butadiene contracts, which corresponds to the geometric changes that occur in the reaction. The lowest positive frequency occurs at 116.73 and corresponds to an asychronus movement of the two ethene carons towards the butadiene ends.

In order to ensure that the transition state had been found the IRC method was used to find the minimum energy pathway to the local minima, which should be the product.
The initial structure looks like the starting material and then the final structure looks like the transition state.

[[Image:ICR butadiene energy graph sp.jpeg|400px| ]][[Image:ICR butadiene rms graph sp.jpeg|400pxpx| ]]

[[Image:ICR initial structure butadiene sp.jpeg|thumb|left|200px|Initial Structure| ]][[Image:ICR final structure butadiene sp.jpeg|thumb|center|200pxpx|Final Structure| ]]

The Molecular orbitals of the transition state were calculated using the AM1 semi-empirical method. The symmetry was determined with respect to the plane of symmetry detailed above.
{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:TS homo sp.jpeg|200px]] || [[Image:TS lumo sp.jpeg|200px]]
|-
| Energy /a.u. || -0.32593 || 0.01842
|-
| Symmetry ||a || s
|}

The HOMO of ethene is the пc-c orbital which has s symmetry and the LUMO is the п*c-c orbital, which has a symmetry. The orbitals of ethene and butadiene can only interact if they have the same symmetry label. Therefore it can be seen that the HOMO of the transition state is made of the HOMO of butadiene and the LUMO of ethene and therefore is antisymmetric. And the LUMO of the transition state is made of the LUMO of butadiene and the HOMO of ethene and is symmetric. The reaction is allowed because the HOMO/LUMO pairs interact and are of similar sizes, so there is significant overlap.

== Malic anhydride + 1,3 Cyclohexadiene ==

[[Image:reaction scheme sp.gif|200px| reaction between malic anhydride + 1,3 cyclohexadiene ]]
The reaction between malic anhydride + 1,3 cyclohexadiene forms mainly the endo product, the reaction is presumed to be kinetically controlled. This can be confirmed by comparing the energies of the transition states.

In order to find the transition states both reactants were optimised at the HF/3-12G level.
{| class="wikitable" border="1"
|+ Optimisation summary
! heading !! Maleic Anhydride || 1,3 Cyclohexadiene
|-
| || [[Image:MA sp.jpeg|thumb|200px|<jmolFile text="Maleic Anhydride">MA sp.mol</jmolFile> ]] ||[[Image:cyclo sp.jpeg|thumb|200px|<jmolFile text="1,3 Cyclohexadiene">cyclo sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -375.10351323 || -230.54323110
|-
| RMS Gradient Norm /a.u.|| 0.00012414 || 0.00004255
|}

The Exo and Endo transition states were optimised by calulating the hessian.
{| class="wikitable" border="1"
|+ Optimisation summary
! !! Exo TS || Endo TS
|-
| || [[Image:exo ts sp3609.jpeg|thumb|200px|<jmolFile text="Exo TS">exo opt sp.mol</jmolFile> ]] || [[Image:endo ts sp3609.jpeg|thumb|200px|<jmolFile text="Endo TS">endo opt sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -605.60359122 || -605.61036815
|-
| RMS Gradient Norm /a.u.|| 0.00001656 || 0.00003160
|}

As can be seen the Exo transition state is higher in energy and so as the endo product is the one that is formed then it can be presumed that the reaction is kinetically controlled. Kinetically controlled reactions go via the lowest energy transition state regardless of whether or not it leads to the lowest energy product. It is generally considered that the stability of the endo transition state is due to steric effects destabilising the exo form and secondary orbital overlap stabilising the endo form.

[[Image:exo ts vib sp.jpeg|left|thumb|200px| Exo TS ]][[Image:endo ts vib sp.jpeg|center|thumb|200px|Endo TS]]
The frequency analysis for both was calculated and the imaginary frequency for the exo t.s. occurs at -647.33 ant for the endo t.s it occurs at -643.57. For both the vibration correspond with the synchronous formation of two bonds between the fragments.

The geometries of the the two structures are given below:

{| class="wikitable" border="1"
| Exo || Endo
|-
| [[Image:exo ts geom sp.jpeg|400px| ]] ||[[Image:endo ts geom sp.jpeg|400px| ]]
|-
| [[Image:exo o geom sp.jpeg|400px| ]] ||[[Image:endo o geom sp.jpeg|400px| ]]
|}
As can be seen both of the geometries are very similar, all the bond lengths ae more or less the same, the only diffenece is the orientation of the two fragments. However in the exo form there may be more steric strain as the hydrogens for the cyclohexadiene are closer to the maleic anhydride. As can be seen in the second pictures the exo form suffers some steric strain as the hydrogens of the CH2-CH2 bringe are close to the malic anhydride. The endo form deosn't sufffer this strain as much as the bridging portion is the double bond CH-CH section, so the hydrogens are further away.

In order to explore the secondary orbtial overlap, the molecular orbitals of the system were calculated using the AM1 semi-empirical method.

{| class="wikitable" border="1"

! !! Exo TS !! !! Endo TS !!
|-
| || HOMO || LUMO || HOMO || LUMO
|-
| ||[[Image:exo homo sp3609.jpeg|200px| ]] || [[Image:exo lumo sp3609.jpeg|200px| ]] ||[[Image:endo homo sp3609.jpeg|200px| ]] || [[Image:endo lumo sp3609.jpeg|200px| ]]
|-
|Energy /a.u|| -0.34113 || -0.04051 || -0.34321 || -0.03567
|}

The HOMO of the endo TS is lower in energy than that of the exo TS. In the endo conformer the p orbitals of the oxygen are in the same region as the π systems. This means that there is an opportunity for mixing, which lowers the energy of the HOMO, stabilising the system. In the exo form the p orbitals of the oxygen are seperated from the π system, so there is no chance of them interacting.

= References =
<references />

File:Anti 2 freq out.out

2011-12-16T13:50:04Z

Sp3609: uploaded a new version of "File:Anti 2 freq out.out"

File:Anti2 2nd opt out.out

2011-12-16T13:50:04Z

Sp3609: uploaded a new version of "File:Anti2 2nd opt out.out"

File:Anti 2 freq out.out

2011-12-16T13:49:22Z

Sp3609: uploaded a new version of "File:Anti 2 freq out.out"

File:Anti2 2nd opt out.out

2011-12-16T13:49:22Z

Sp3609:

Rep:Mod:sp33

2011-12-16T13:45:30Z

Sp3609: /* optimising the reactant and product */

= Cope Rearrangement =
The cope rearrangement was discovered by A. Cope and E. Hardy in 1939<ref>A.Cope et al, ''J. Am. Chem. Soc.'', 1940, 62, 441-444 {{DOI|10.1021/ja01859a055}}</ref>The reaction is a [3,3] sigmatropic reaction that has been proven to occur concertedly.<ref>O. Wiest, A.Kersey, et. al; ''J. Am. Chem. Soc.''; 1994, '''116''', 10336-10337{{DOI|10.1021/ja00101a078}}</ref>
[[Image:copeschemesp.gif|300px| ]]

It is generally accepted that the reaction goes via a chair or boat like transition state.

[[Image:TSsp.gif|300px| ]]

The low-energy minima and transition structures on the C6H10 potential energy surface can be found, in order to determine the preferred reaction mechanism.

== optimising the reactant and product ==

A molecule of 1,5 hexadiene (1) was drawn using gaussian with an anti linkage of the main chain. It was then optimised using the HF/3-21G method and then the energy and symmetry were recorded in the table below. A gauche conformer (2) of the molecule was also optimised and analysed. The gauche conformer was lower in energy . In order to calculate the activation energies and enthalpies the lowest energy conformer is needed. Because the Gauche conformer is lower in energy, it would make sense to try structures with more gauche conformations in them. Several structures were tried to see which was lowest in energy. They were then identified by comparing to the low energy conformers in [[Mod:phys3#Appendix 1|Appendix 1]] .

{| class="wikitable" border="1"

! !! conformer !!Energy /a.u !! Energy /Kcalmol-1 !! Point Group !! Conformation
|-
| 1 || [[Image:conformer 1sp.jpeg|thumb|100px|<jmolFile text="Conformer 1">confomer1sp.mol</jmolFile> ]] || -231.69097 || -145388.28 || C1 || anti 4
|-
| 2 || [[Image:conformer 2sp.jpeg|thumb|100px|<jmolFile text="Conformer 2">confomer2sp.mol</jmolFile> ]]|| -231.68962 || -145387.43 || C1 || gauche 5
|-
| 3 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Conformer 3">confomer3sp.mol</jmolFile> ]] || -231.69260 || -145389.30 || C2 || anti 1
|-
| 4 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Conformer 4">confomer4sp.mol</jmolFile> ]] || -231.69266 || -145389.34 || C1 || gauche 3
|-
| 5 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Conformer 5">confomer5sp.mol</jmolFile> ]] || -231.69254 || -145389.26 || Ci || anti 2

|}

The lowest energy conformation is the gauche 3 conformation followed by the anti 1 conformation. The introduction of the gauche linkage means the molecule is more stable as there are now more favorable van der Waahls interactions.
The lowest three conformations were then optimised at the B3LYP/6-31G* level, as this is a more powerful technique and gives more accurate energies.

{| class="wikitable" border="1"

! conformer !! Energy /a.u !! Energy /Kcalmol-1 || input structure || output structure
|-
| Gauche 3|| -234.61133 || -147220.83 || [[Image:conformer 4sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">confomer4sp.mol</jmolFile> ]] || [[Image:gauche3sp.jpeg|thumb|100px|<jmolFile text="Gauche 3">gauche3sp.mol</jmolFile> ]]
|-
| Anti 1 || -234.61179 || -147221.12 || [[Image:conformer 3sp.jpeg|thumb|100px|<jmolFile text="Anti 1">confomer3sp.mol</jmolFile> ]] || [[Image:anti1sp.jpeg|thumb|100px|<jmolFile text="Anti 1">anti1sp.mol</jmolFile> ]]
|-
| Anti 2 || -234.61171 || -147221.07 || [[Image:conformer 5sp.jpeg|thumb|100px|<jmolFile text="Anti 2">confomer5sp.mol</jmolFile> ]] || [[Image:anti2sp.jpeg|thumb|100px|<jmolFile text="Anti 2">anti2sp.mol</jmolFile> ]]
|}
When calculated at this higher level the energies of the three conformers change and the anti 1 conformer is now the lowest in energy. As can be seen from the images there isn't a large difference between the structures from the two levels of optimisation.

When the reaction occurs it goes from the Ci symmetry conformer. Therefore the geometries from the two calculations can be compared directly.

{| class="wikitable" border="1"

! method !! Bond lengths/Å and Angles /°
|-
| HF/3-21G ||[[Image:cibondsp.jpeg|400px| ]]
|-
| B3LYP/6-31G* ||[[Image:ci2bondssp.jpeg|400px| ]]
|}
The bond lengths are very similar but the angles are relatively different. with the B3LYP structure being slightly more linear.

The frequency analysis of this conformer was performed to ensure that a true minima had been found.
[[Image:IR anti2sp.jpeg|thumb|center|400px| Ci conformer ]]
As can be seen in the spectra, there are no negative vibrations, so it is confirmed that an actual minima has been found as oppose to a transition atate maxima.

The various energies of the system are also calculated using this method. The sum of the electronic and zero point energies is the potential energy at 0K. The sum of electronic and thermal energies gives the energy at 298.15K and 1 atmosphere. It contains contributions from the translational, rotational and vibrational energies. The third gives the enthalpy and takes into a correction for room temperature as H = E + RT. The fourth is the energy with the entropic contribution to the free energy considered. The final three are calculated at 298.15K and all energies are given in atomic units.

{| class="wikitable" border="1"

! !! a.u. !! kJmol-1
|-
| Sum of electronic and zero point energies || -234.469204 || -615599
|-
| Sum of electronic and thermal energies || -234.461857 || -615580
|-
| Sum of electronic and thermal enthalpies || -234.460913 || -615577
|-
| Sum of electronic and thermal free energies || -234.500777 || -615682
|}
File:Gauche out.out: File uploaded.

File:Anti out.out: File uploaded.

File:Anti confomer 2nd.out: File uploaded.

File:Gauche 3rd confomer.out: File uploaded.

File:Anti confomer 2 ci.out: File uploaded.

File:Anti 3rd.out: File uploaded.

File:2nd gauche confomer.out: File uploaded.

File:Anti 1 freq out.out: File uploaded.

File:Anti 2 freq out.out: File uploaded.

File:Anti1 2ndopt out.out: File uploaded.
Calculation files: https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Gauche_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti_out.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Anti confomer 2nd.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:.out
https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:.out

== Optimising the Transition States ==
=== Chair Transition States ===

To begin with an allyl fragment was optimised at the HF/3-21G level. Two of these fragments were then combined to give an initial structure for the chair T.S. The two fragments were placed with the ends of the allyl fragments 2.2Å apart and then optimised using in two different ways.

The first method calculates the force constant matriix in order to find the position of the T.S. The structure was optimised and the frequency analysis in one step.[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S 1">chair ts opt 1.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932246
|-
| RMS Gradient Norm /a.u.|| 0.00001378
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -818.97 which corresponds to the formation of one bond and breaking of the other.

[[Image:chairvib1sp.jpeg|300px| ]]

The second method uses a frozen co-ordinate method. The two allyl fragments were optimised with the two ends frozen at 2.2Å at the HF/3-21G level and then again with then bonds unfrozen. [[Image:chair ts otheropt part 2.jpeg|thumb|300px|<jmolFile text="Chair T.S 2">chair ts opt 2.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.61932189
|-
| RMS Gradient Norm /a.u.|| 0.00005807

|}

The geometries of the two optimised transition states are compared in the table below

{| class="wikitable" border="1"

! !! 1st Method || 2nd Method
|-
| C-C bond formed/broken || 2.02 || 2.02
|-
| other C-C bonds || 1.389 || 1.389
|}

They both give identical transition state geometries so either can be used depending on how much information about the transition state is known.

=== Boat Transition State ===
The Boat T.S was optimised using the QST2 method. This takes the reactant structure and product structure and extrapolates between the two, to find the transition state.The two structures were positioned so they are similar to a boat conformation and then optimised. [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat ts">QST2 opt.mol</jmolFile> ]]

{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60279992
|-
| RMS Gradient Norm /a.u.|| 0.00013432
|-
| Imaginary Freq || 1
|}

There is one imaginary frequency at -840.35 which corresponds to the formation of one bond and breaking of the other.

[[Image:boat higher vib sp.jpeg|300px| ]]

The bonds that are being formed are 2.14Å and the other C-C bonds are 1.382Å.

=== Intrinsic reaction co-ordinate ===

From looking at the transition states, its near on impossible to tell which conformer the reaction path will lead to. However using the IRC method the minimum energy path to the nearest minima can be followed. Because the reaction is symmetric it only needs to be run in the forward reaction.

This was initially done with 50 points along the pathway, however that didn't lead to a minima, so it was run again with 100 points.

{| class="wikitable" border="1"

! Points along the IRC !! Energy Graph !! RMS gradient Graph || Inital Structure || Final Structure
|-
| 50 || [[Image:chair icr 1 energy graph.jpeg|200px| ]] || [[Image:chair icr 1 rms graph.jpeg|200px| ]] || [[Image:icr 1 initial.jpeg|200px| ]] || [[Image:icr 1 final.jpeg|200px| ]]
|-
| 100 || [[Image:ICR 2 chair energy graph.jpeg|300px| ]] || [[Image:ICR 2 chair rms graph.jpeg|300px| ]] || [[Image:icr 2 initial.jpeg|200px| ]] || [[Image:icr 2 final.jpeg|200px| ]]
|}

As can be seen the gradient doesn't reach zero, even for 100 points, and the final structure is almost identical. In order to get further the force constants may need to be calculated at every step instead of just once.

== Calculating Activation Energies ==

To calculate the activation energies of the reaction via each transition state the transition states need to be optimised at a higher level to give more accurate energies. Therefore both were optimised at the B3LYP/6-31G* level.

{| class="wikitable" border="1"
|+ Chair T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure ||[[Image:chair1sp.jpeg|thumb|300px|<jmolFile text="Chair T.S ">chair ts opt 1.mol</jmolFile> ]] || [[Image:chair higher opt.jpeg|thumb|300px|<jmolFile text="Chair T.S">chair higher opt.mol</jmolFile> ]]
|-
| Energy || -231.619322 || -234.55698
|-
| new c-c bond lengths /Å || 2.02 || 1.97
|-
| other bond length /Å || 1.38 || 1.41
|-
| Frequency of imaginary vibration || -818.97 || -565.54
|}
{| class="wikitable" border="1"
|+ Boat T.S
! !! HF/!! B3LYP/6-31G*
|-
| Structure || [[Image:boat qst2 opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">QST2 opt.mol</jmolFile> ]] || [[Image:boat higher opt sp.jpeg|thumb|300px|<jmolFile text="Boat TS">boat higher opt sp.mol</jmolFile> ]]
|-
| Energy || -231.602799 || -234.54309
|-
| new c-c bond lengths /Å || 2.14 || 2.21
|-
| other bond length /Å || 1.38 || 1.39
|-
| Frequency of imaginary vibration || -840.35 || -530.36
|}

As can be seen, the geometries are relatively similar but the energies are very different.
A summary of the energies is given below:

{| class="wikitable" border="1"

! !! Electronic energy !! Sum of electronic and zero point energies !! Sum of electronic and thermal energies !! Sum of electronic and thermal enthalpies !! Sum of electronic and thermal free energies
|-
| Reactant || -234.611710 || -234.469204 || -234.461857 || -234.460913 || -234.500777
|-
| Chair T.S || -234.556983 || -234.414929 || -234.409008 || -234.408064 || -234.443814
|-
| Boat T.S || -234.543093 || -234.402342 || -234.396008 || -234.395063 ||-234.431752
|}

The Activation Energy of the reaction can be calculated by Eactivation = Etransition state - Ereactants

To calcultate the Activation Energy at rooom temperature 298.15 K then the sum of the electronic and thermal energies should be used. To calculate it at 0K then the sum of electronic and zero point energies should be used.

Chair Transition State
@ 298.15 KEactivation = -234.409008- -234.461857 = 0.052849 au = 33.16 kcalmol-1
@ 0 KEactivation = -234.414929- -234.469204 = 0.054275 au = 34.06 kcalmol-1
Boat Transition State
@ 298.15 KEactivation = -234.396008- -234.461857 = 0.065849 au = 41.32 kcalmol-1
@ 0 KEactivation = -234.402342- -234.469204 = 0.066862 au = 41.96 kcalmol-1

The reaction that goes via a Chair Transition State has a lower activion energy and is therefore the way the reaction proceeds.

The experimental values for the activation energy via a chair transition state is 33.5 kcalmol-1 and via the boat transition state 44.7 kcalmol-1. The calculated values are in very close agreement with the experimental values.

= Diels-Alder Cycloaddition =
The Diels Alder reaction is a [4+2] cycloaddition. The reaction was discovered in 1928 by Otto Diels and Kurt Alder.<ref>Diels, O. Alder, K.; ''Justus Liebig's Annalen der Chemie''; 1928; '''460'''; 98–122.{{DOI|10.1002/jlac.19284600106}}</ref>
The reaction can be very stereo and regio specific depending on the elctronics and sterics of the reactants used.

Two different reactions will be looked at below:
1) the reaction between Cis butadiene and Ethene. This is the simplest Diels-Alder reaction possible, there are no side groups to influence the reaction sterically or electronicly, so the basics interactions of the reaction can be clearly seen.
2) the reaction between Malic anhydride + 1,3 Cyclohexadiene. This is more complex, as both the steric effect of the briding section and the electronic effect of the functionalised dienophile must be considered.

==Cis Butadiene and ethene ==

[[Image:butadiene reaction scheme sp.gif|thumb|widthpx| ]]

Cis butadiene was optimised at the HF/3-21G level.
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FOPT
|-
| Calculation Method ||RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -154.05394317
|-
| RMS Gradient Norm /a.u.|| 0.00007352
|}

The HOMO and LUMO were then calculated using the AM1 semi-empirical MO method.[[Image:butadiene plane sp.gif|thumb|200px|Plane of symmetry ]]

{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:butadiene homo sp.jpeg|200px]] || [[Image:butadiene lumo sp.jpeg|200px]]
|-
| Energy /a.u.|| -0.35083 || 0.01977
|-
| Symmetry || a || s
|}

The symmetry of the orbitals are determined with respect to the plane which runs through the center of the middle bond .
If the orbital is symmetric with respect to reflection in the plane, then it is labeled s and if not it is labeled a.

The transition state for the reaction has an envelope-like structure. It was drawn in gaussview with the ends of the two fragments positioned 2.2Å apart. The transition structure was optimised using at the HF/3-21G level using the QST2 method.
[[Image:transition state sp.jpeg|thumb|200px|<jmolFile text="Butadiene + ethene T.S">TS sp3609.mol</jmolFile> ]]
{| class="wikitable" border="1"
|+ Optimisation summary

|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| E(RHF)/a.u.|| -231.60320837
|-
| RMS Gradient Norm /a.u.|| 0.00002624
|-
| Imaginary frequencies || 1
|}

[[Image:transition state geometry sp.jpeg|200px| ]]

The various bond lengths and angels of the transition state are detailed above. Typical sp3 c-c bonds are ~1.54Å and sp2 c-c bonds are ~1.33Å. The Van der Waahls radius of carbon is 1.70Å<ref>A. Bondi; ''J. Phys. Chem.'', 1964, '''68 (3)''', pp441–451 {{DOI|10.1021/j100785a001}}</ref> The σ bonds that are long compared to a σ bond, but the bonds in the cis butadiene are all approximately equal. This suggests that the starting point of the change in structure is a change in the electronic structure rather than the formation of new bonds.

[[Image:transition vibration sp.jpeg|thumb|100px| ]]The imaginary frequency occurs at -818.34 and corresponds to the formation of two new bonds in a synchronous fashion. As the new bonds form, the double bonds lengthen and the single bond in the butadiene contracts, which corresponds to the geometric changes that occur in the reaction. The lowest positive frequency occurs at 116.73 and corresponds to an asychronus movement of the two ethene carons towards the butadiene ends.

In order to ensure that the transition state had been found the IRC method was used to find the minimum energy pathway to the local minima, which should be the product.
The initial structure looks like the starting material and then the final structure looks like the transition state.

[[Image:ICR butadiene energy graph sp.jpeg|400px| ]][[Image:ICR butadiene rms graph sp.jpeg|400pxpx| ]]

[[Image:ICR initial structure butadiene sp.jpeg|thumb|left|200px|Initial Structure| ]][[Image:ICR final structure butadiene sp.jpeg|thumb|center|200pxpx|Final Structure| ]]

The Molecular orbitals of the transition state were calculated using the AM1 semi-empirical method. The symmetry was determined with respect to the plane of symmetry detailed above.
{| class="wikitable" border="1"

! !!HOMO !! LUMO
|-
| ||[[Image:TS homo sp.jpeg|200px]] || [[Image:TS lumo sp.jpeg|200px]]
|-
| Energy /a.u. || -0.32593 || 0.01842
|-
| Symmetry ||a || s
|}

The HOMO of ethene is the пc-c orbital which has s symmetry and the LUMO is the п*c-c orbital, which has a symmetry. The orbitals of ethene and butadiene can only interact if they have the same symmetry label. Therefore it can be seen that the HOMO of the transition state is made of the HOMO of butadiene and the LUMO of ethene and therefore is antisymmetric. And the LUMO of the transition state is made of the LUMO of butadiene and the HOMO of ethene and is symmetric. The reaction is allowed because the HOMO/LUMO pairs interact and are of similar sizes, so there is significant overlap.

== Malic anhydride + 1,3 Cyclohexadiene ==

[[Image:reaction scheme sp.gif|200px| reaction between malic anhydride + 1,3 cyclohexadiene ]]
The reaction between malic anhydride + 1,3 cyclohexadiene forms mainly the endo product, the reaction is presumed to be kinetically controlled. This can be confirmed by comparing the energies of the transition states.

In order to find the transition states both reactants were optimised at the HF/3-12G level.
{| class="wikitable" border="1"
|+ Optimisation summary
! heading !! Maleic Anhydride || 1,3 Cyclohexadiene
|-
| || [[Image:MA sp.jpeg|thumb|200px|<jmolFile text="Maleic Anhydride">MA sp.mol</jmolFile> ]] ||[[Image:cyclo sp.jpeg|thumb|200px|<jmolFile text="1,3 Cyclohexadiene">cyclo sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -375.10351323 || -230.54323110
|-
| RMS Gradient Norm /a.u.|| 0.00012414 || 0.00004255
|}

The Exo and Endo transition states were optimised by calulating the hessian.
{| class="wikitable" border="1"
|+ Optimisation summary
! !! Exo TS || Endo TS
|-
| || [[Image:exo ts sp3609.jpeg|thumb|200px|<jmolFile text="Exo TS">exo opt sp.mol</jmolFile> ]] || [[Image:endo ts sp3609.jpeg|thumb|200px|<jmolFile text="Endo TS">endo opt sp.mol</jmolFile> ]]
|-
| Calculation Type || FOPT || FOPT
|-
| Calculation Method || RHF || RHF
|-
| Basis Set || 3-21G || 3-21G
|-
| E(RHF)/a.u.|| -605.60359122 || -605.61036815
|-
| RMS Gradient Norm /a.u.|| 0.00001656 || 0.00003160
|}

As can be seen the Exo transition state is higher in energy and so as the endo product is the one that is formed then it can be presumed that the reaction is kinetically controlled. Kinetically controlled reactions go via the lowest energy transition state regardless of whether or not it leads to the lowest energy product. It is generally considered that the stability of the endo transition state is due to steric effects destabilising the exo form and secondary orbital overlap stabilising the endo form.

[[Image:exo ts vib sp.jpeg|left|thumb|200px| Exo TS ]][[Image:endo ts vib sp.jpeg|center|thumb|200px|Endo TS]]
The frequency analysis for both was calculated and the imaginary frequency for the exo t.s. occurs at -647.33 ant for the endo t.s it occurs at -643.57. For both the vibration correspond with the synchronous formation of two bonds between the fragments.

The geometries of the the two structures are given below:

{| class="wikitable" border="1"
| Exo || Endo
|-
| [[Image:exo ts geom sp.jpeg|400px| ]] ||[[Image:endo ts geom sp.jpeg|400px| ]]
|-
| [[Image:exo o geom sp.jpeg|400px| ]] ||[[Image:endo o geom sp.jpeg|400px| ]]
|}
As can be seen both of the geometries are very similar, all the bond lengths ae more or less the same, the only diffenece is the orientation of the two fragments. However in the exo form there may be more steric strain as the hydrogens for the cyclohexadiene are closer to the maleic anhydride. As can be seen in the second pictures the exo form suffers some steric strain as the hydrogens of the CH2-CH2 bringe are close to the malic anhydride. The endo form deosn't sufffer this strain as much as the bridging portion is the double bond CH-CH section, so the hydrogens are further away.

In order to explore the secondary orbtial overlap, the molecular orbitals of the system were calculated using the AM1 semi-empirical method.

{| class="wikitable" border="1"

! !! Exo TS !! !! Endo TS !!
|-
| || HOMO || LUMO || HOMO || LUMO
|-
| ||[[Image:exo homo sp3609.jpeg|200px| ]] || [[Image:exo lumo sp3609.jpeg|200px| ]] ||[[Image:endo homo sp3609.jpeg|200px| ]] || [[Image:endo lumo sp3609.jpeg|200px| ]]
|-
|Energy /a.u|| -0.34113 || -0.04051 || -0.34321 || -0.03567
|}

The HOMO of the endo TS is lower in energy than that of the exo TS. In the endo conformer the p orbitals of the oxygen are in the same region as the π systems. This means that there is an opportunity for mixing, which lowers the energy of the HOMO, stabilising the system. In the exo form the p orbitals of the oxygen are seperated from the π system, so there is no chance of them interacting.

= References =
<references />

File:Anti1 2ndopt out.out

2011-12-16T13:43:15Z

Sp3609:

File:Anti 2 freq out.out

2011-12-16T13:43:15Z

Sp3609:

File:Anti 1 freq out.out

2011-12-16T13:43:14Z

Sp3609:

File:2nd gauche confomer.out

2011-12-16T13:43:14Z

Sp3609:

File:Anti 3rd.out

2011-12-16T13:43:13Z

Sp3609:

File:Anti confomer 2 ci.out

2011-12-16T13:43:13Z

Sp3609:

File:Gauche 3rd confomer.out

2011-12-16T13:43:12Z

Sp3609:

File:Anti confomer 2nd.out

2011-12-16T13:43:12Z

Sp3609:

File:Anti out.out

2011-12-16T13:43:11Z

Sp3609:

File:Gauche out.out

2011-12-16T13:43:11Z

Sp3609:

File:Chair ts opt 2.mol

2011-12-16T13:39:22Z

Sp3609: uploaded a new version of "File:Chair ts opt 2.mol"

File:Chair ts opt 1.mol

2011-12-16T13:39:07Z

Sp3609: uploaded a new version of "File:Chair ts opt 1.mol"

File:Chair higher opt.mol

2011-12-16T13:38:52Z

Sp3609:

File:QST2 opt.gjf

2011-12-16T13:36:41Z

Sp3609: