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==Module 3==

===Optimizing the Reactants and Products===

====Antiperiplanar Arrangement:====

[[File:REACT ANTI2.LOG]]

[[File:React anti2.JPG|400px]]

Summary:

[[File:React anti2 summary.JPG]]

The final structure does show some symmetry as there is a line of symmetry across the xy plane. This is so that the atoms can have the least steric hindrance possible. The symmetry labels recorded are C<sub>i</sub>.

====Gauche Conformation:====

[[File:REACT GUACHE.LOG]]

[[File:React guache.JPG|400px]]

Summary:

[[File:React guache summary.JPG]]


The symmetry shown is C1.

====Activation energies and Enthalpies====

Calculated activation energies and enthalpies use the lowest energy conformation of a reactant molecule as a reference. As such it will be conformation which has the least steric repulsions and the most stabilizing orbital interactions. From the energies calculated above for app and gauche, it can be seen that app, is going to be lowest energy conformer.

====Compare structures in Appendix 1 with optimized structures====


From the APP optimization which gives the energy as -231.69253528 a.u this compares very well with the anti2 conformation given in appendix 1. The value given in appendix 1 is -231.69254 a.u. As such the low energy conformer of 1,5-hexadiene is C<sub>i</sub>.

For the gauche conformation, the energy given is -231.68771617 a.u. This compares to the gauche 1 conformer in appendix 1. The value given in appendix one is -231.68772 a.u. As such this low energy conformer of 1,5-hexadiene is C<sub>2</sub>.


[[File:Appendix 1.jpg]]

The energy comparison between the optimized C<sub>i</sub> molecule (-231.69253528 a.u) and the one shown in appendix 1 (-231.69254 a.u.) is 4.72x10<sup>-6</sup> a.u. This is relatively small compared to the size of the energies and as such shows us that the final energies calculated using optimization are very close to the true value.

====Optimized using B3LYP/6-31G*====

[[File:REACT DFT.LOG]]

Summary:

[[File:React DFT.JPG]]

As can be seen from the summary table, the total energy is much less using this method for calculation.
Using the HF/3-21G the energy is: -231.69253528 a.u
Using DFT/6-31G*, the energy is: -234.57111700 a.u

From this we can see that there is a 2.87858172 a.u difference which is huge. Although these figures can not be compared directly, it shows that the higher level of theory calculation has found the lower energy conformer.

As can be seen from the summary the symmetry is given as C<sub>i</sub> without the need for us to manually ask the program to give it a symmetry label for us. As such, there is a change in overall geometry, however this is not very big.

====Frequency Calculation====

[[File:REACT DFT FREQ.LOG]]

[[File:React DFT freq summary.JPG]]

 Sum of electronic and zero-point Energies=           -234.428083
 Sum of electronic and thermal Energies=              -234.420769
 Sum of electronic and thermal Enthalpies=            -234.419825
 Sum of electronic and thermal Free Energies=         -234.459745



===Optimizing the 'Chair' Transition Structures===

====Optimized allyl fragment====

[[File:ALLY HF OPT.LOG]]

Summary:

[[File:Ally HF opt summary.JPG]]

<jmol><jmolApplet>  <title>test molecule</title>  <color>black</color>  <size>200</size>  <uploadedFileContents>Ally HF opt.mol</uploadedFileContents> </jmolApplet></jmol>


The Chair guess can be found here:
[[File:Chair ts guess.gjf]]

This is the file where the 2 optimized CH2CHCH2 molecules are ~2.2 Armstrongs apart.


====The optimized chair using method: opt+freq and Optimization to a TS (Berny)====

[[File:CHAIR OPTFREQ.LOG]]

[[File:Chair optfreq summary.JPG]]


The optimized structure has a frequency of magnitude ~818cm<sup>-1</sup> shown here:

[[File:Chair optfreq 818freq.JPG]]

<jmol><jmolApplet>  <title>test molecule</title>  <color>black</color>  <size>200</size>  <uploadedFileContents>Chair optfreq.mol </uploadedFileContents> </jmolApplet></jmol>


The optimized molecule has terminal C-C bond breaking/forming bonds at average: 2.020355 Angstroms.

====The optimized chair using method: Optimization with Redundant Coord Editor and co-ordinates frozen.====

[[File:CHAIR REDUNANDANCE3.LOG]]

[[File:Chair redunandance3.JPG|400px]]

[[File:Chair_redunandance3_summary.JPG]]

In the above method, the optimized structure looks similar to the transition optimized using the TS (Berny). However the bond forming/breaking distances were fixed to ~2.2 Armstrongs. Average terminal C-C bond distance is 2.156475 Angstroms.  However these can now be optimized to give:

This is done by changing the terminal C-C bond atoms to have a derivative setting during optimization.

[[File:CHAIR REDUNANDANCE3 PART2.LOG]]

[[File:Chair opt redundance3 part2.JPG|400px]]

[[File:Chair_opt_redundance3_part2_summary.JPG]]

The Average terminal carbon bond separation is: 2.02058 angstroms.

====Comparison====

{| class="wikitable" border="1"
|+ Comparison between TS (Berny) Optimization and Frozen Cooord Optimization
! !!TS (Berny) Optimization !! Frozen Cooord Optimization!!
|-
| Terminal C-C separation (angstroms)||2.020355 ||2.02058
|-
|Total Energy (a.u)|| -231.61932247|| -231.61932192
|}

From the structure we can see the big difference is that in the TS(Berny)Optimization there are 4 bonds observed which are each of a 1.5 bond order. However in the Frozen Coord Optimization there is 2 double bonds and 2 single bonds. What this means is the electron density has been concentrated to one side of the molecule and it is at this side of the molecule that the terminal C-C bonds are likely to form first.

However if we look at the C-C separation, for both methods, the separation does not change very much. What this implies is that both models have taken into account factors such as orbital overlaps and steric hindrances, to get the optimized bond lengths.

The energies differ only at the 6th decimal point, and from this we can say that both are low energy conformers.

===Optimizing the 'Boat' Transition Structures===

Firstly labeling of the reactant and product atoms must be done:

[[File:BOAT QST2.LOG]]

[[File:Boat QSt2 before optimization.JPG|400px]]

Using the QST2 optimization method we get:

[[File:Boat QST2.JPG|400px]]

Summary:

[[File:Boat Qst2 summary.JPG|400px]]

As can be seen here, Guassian has failed as it did not rotate around the central bonds. As such the bonds have been elongated and are crossing which is unrealistic. If  this is to work then the c-c-c-c of the reactant molecule the dihedral angle must be 0 degrees. The inside c-c-c must be reduced to 100 degrees shown below:

[[File:BOAT QST2 ANGLED2.LOG]]

The optimized molecule shows this:

[[File:Boat Qst2 angled2.JPG|400px]]

Summary:

[[File:Boat Qst2 angled2 summary.JPG]]

The imaginary frequency is as follows:

[[File:Boat qst2 angled2 freq.JPG]]

====Iintrinsic Reaction Co-ordinate (IRC)====

The IRC  is the method which allows us to follow the minimum energy path from a transition structure down to its local minimum on a potential surface. I will now optimize the chair transition structure and using IRC with 50 points in the forward direction.

[[File:Log 65092.log]]

[[File:Chair IRC output4.gif]]

[[File:Chair irc4 energy.JPG|800px]]

[[File:Chair irc4 gradient.JPG|800px]]

Lowest energy = -231.69157536 a.u

From the above information it can be seen that there this has given the formation of the bond, but more is needed, as the gradient is still not steady. ie. the calculation has not finished. As such to reach the minimum geometry I will recalculate the force constants after each point.

[[File:Chair IRC output.log]]

[[File:Chair IRC output.gif]]

[[File:Chair IRC energypath.JPG|800px]]

[[File:Chair IRC gradient.JPG|800px]]

The lowest energy from the plot is:
-231.69157878 a.u

This is true as from the plot we can see that the gradient evens out which means the minimum has been reached. Thus this is the lowest energy.

====Calculate the activation energies====

Chair frequency analysis at HF/3-21G
 Sum of electronic and zero-point Energies=           -231.466700
 Sum of electronic and thermal Energies=              -231.461341
 Sum of electronic and thermal Enthalpies=            -231.460397
 Sum of electronic and thermal Free Energies=         -231.495206

Boat frequency analysis at HF/3-21G
 Sum of electronic and zero-point Energies=           -231.450929
 Sum of electronic and thermal Energies=              -231.445300
 Sum of electronic and thermal Enthalpies=            -231.444356
 Sum of electronic and thermal Free Energies=         -231.479775


Chair conformer using B3LYP/6-31G*

[[File:CHAIR OPTFREQ 6-31G.LOG]]

[[File:CHair_opt_6-31G_summary.JPG‎]]

Once symmetry has been done on it, it is C2h symmetry.

 Sum of electronic and zero-point Energies=           -234.369094
 Sum of electronic and thermal Energies=              -234.362667
 Sum of electronic and thermal Enthalpies=            -234.361723
 Sum of electronic and thermal Free Energies=         -234.398934


Boat Conformer optimised using B3LYP/6-31G*

[[File:BOAT_FREQ_6-31G.LOG]]

[[File:Boat_freq_6-31G_summary.JPG‎]]

Once symmetry has been performed, it gives C2v symmetry.

 Sum of electronic and zero-point Energies=           -234.356893
 Sum of electronic and thermal Energies=              -234.351048
 Sum of electronic and thermal Enthalpies=            -234.350104
 Sum of electronic and thermal Free Energies=         -234.385687

{| class="wikitable" border="1"
|+ Thermochemistry results and Activation energies for Chair confomer
! !!HF, 3-21G !! HF 3-21G!! B3LYP/6-31G !! EB3LYP/6-31G!!
|-
! !!E<sub>elec</sub> + ZPE  !! E<sub>elec</sub> +E<sub>therm</sub> !! E<sub>elec</sub> + ZPE  !! E<sub>elec</sub> +E<sub>therm</sub> !!
|-
| Anti 2 a.u||  -231.539539  ||-231.532565 || -234.428083  ||-234.420769
|-
|Chair TS a.u|| -231.466700|| -231.461341||-234.369094  ||-234.362667
|-
| Eact a.u||0.072839 ||0.071224|| 0.058989|| 0.058102
|-
|Eact Kcal-1|| 45.70712805|| 44.83614902|| 37.0161284 ||36.45952792
|}

{| class="wikitable" border="1"
|+ Thermochemistry results and Activation energies for Boat confomer
! !!HF, 3-21G !! HF 3-21G!! B3LYP/6-31G !! EB3LYP/6-31G!!
|-
! !!E<sub>elec</sub> + ZPE  !! E<sub>elec</sub> +E<sub>therm</sub> !! E<sub>elec</sub> + ZPE  !! E<sub>elec</sub> +E<sub>therm</sub> !!
|-
| Anti 2 a.u||  -231.539539  ||-231.532565 || -234.428083  ||-234.420769
|-
|Chair TS a.u|| -231.450929|| -231.445300||-234.356893  ||-234.351048
|-
| Eact a.u||0.08861 ||0.087265|| 0.07119|| 0.069721
|-
|Eact Kcal-1|| 55.60357249|| 54.75957289||44.67236571 ||43.75055499
|}

From the table we can see that generally the Chair conformer has lower activation energies than the Boat conformer. This is due to less steric repulsions and better orbital overlaps. The bond angles will be less strained in the chair conformation and as such will be lower in energy and require less activation energy than the boat. The instructions give, experimental values of 33.5 ± 0.5 kcal/mol for the chair and 44.7 ± 2.0 kcal/mol for the boat at 0K. For both the chair and the boat the answers are relatively close, and the trend is immediately obvious. As such Guassian is a good guide to the energy predictions. On top of that it can be seen that the method of B3LYP/6-31G is much better than HF/3-21G in both the chair and boat conformations.

===Diels Alder Conformations===

All optimizations in this section will be done using AM1 semi-empirical optimization.

====Cis Butadiene Optimize====

CisButadiene was optimized using the AM1 method.

[[File:BUTADIENE_OPT_AM1.LOG]]
<jmol><jmolApplet>  <title>test molecule</title>  <color>black</color>  <size>200</size>  <uploadedFileContents>Butadiene_opt_AM1.mol</uploadedFileContents> </jmolApplet></jmol>

Summary:

[[File:Butadiene_opt_AM1_summary.JPG]]

HOMO of the cis butadiene at energy: -0.34382 a.u and asymmetric

[[File:Butadiene_opt_AM1_HOMO.JPG|400px]]


LUMO of the cis butadiene at energy: 0.01709 a.u and symmetric

[[File:Butadiene_opt_AM1_LUMO.JPG]]

====Diene Transition Stat geometry====

The computation of the Transition state geometry was done, which maximizes the overlap between the ethylene pi orbitals and the pi system on the butadiene.

[[File:Diels_TS.JPG|400px]]

Product optimized.

[[File:Diels_optfreq_product.JPG|400px]]

Log file: [[File:Log_65175.log]]

This has the HOMO at -0.39167 a.u and has a D2/ C1 symmetry.

[[File:Diels AM1 HOMO.JPG|400px]]

The LUMO is at 0.13460

[[File:Diels_AM1_LUMO.JPG|400px]]

For the above calculations, an AM1 method was carried out with a guess bong length between ethene and butadiene as 1.8 angstroms. The molecule was drawn firstly from a bicyclo system and removing the CH2-CH2 fragment. The C-C bond lengths in the diels alder reaction have a bond length of 1.54766 angstroms.

Typical Sp<sup>3</sup C-C bondlengths are 1.54 Angstroms and Sp<sup>2</sup> C=C bond lengths are 1.35520 angstroms. The van der Waals radius of a C atom is 1.7 angstroms. From this information we can say that the C-C bond in the TS is much shorter than the typical C-C bond. Also there will be steric hindrance as it exceeds the VDW radius.<ref name="LazyDog" /> 

The Vibration which corresponds to the TS at -91.85 cm-1 is:

[[Diels_vibration.JPG‎|400px]]

This is asynchronous as compares when compared to the lowest positive frequency: 224.76cm-1 we can see that the intensity of the IR is much bigger, which means it has a much bigger effect on the structure.

The HOMO at the transition structure is anti symmetric and uses the HOMO from ethene and the LUMO from cis butadiene. This is deduced from the fact that the HOMO of one reactant must react with the LUMO of another and from looking at the HOMO and LUMO complexes.

====Study the regio-selectivity====

Firstly we need to optimize the Cyclohexa-1,2-diene molecule.

Cyclohexa-1,2-diene

[[File:Cyclohe-diene opt.JPG|400px]]

Summary:

[[File:Cyclohexa-diene opt summary.JPG]]

[[File:Cyclohexadine_opt.log]]

Bond length of partly formed C-C bond: 1.48178 angstroms

The HOMO is -0.32074 and anti symmetric

[[File:Cyclohe-diene_HOMO.JPG|400px]]

The LUMO is 0.01692 and symmetric with respect to the plane

[[File:Cyclohexa-diene_LUMO.JPG|400px]]

Symmetry is C2V


Then we need to optimize maleic anhydride.

[[File:Log 65221.log]]

[[File:Maleic opt AM1.JPG|400px]]

Summary:

[[File:Maleic_opt_AM1_summary.JPG]]

The HOMO is given at: -0.44187 and symmetric

[[File:Maleic opt AM1 HOMO.JPG|400px]]

The LUMO is given at: -0.05949 and asymmetric

[[File:Maleic opt AM1 LUMO.JPG|400px]]

====ENDO Form====

To form this, I will use the freeze method.

[[File:Endo freeze4.log]]

[[File:Endo freeze4.JPG|400px]]

Summary:

[[File:Endo freeze4 summary.JPG]]

The C-C bonds were then set to derivative.


[[File:Endo deriv4.log]]

[[File:Endo deriv4.JPG|400px]]

Summary:

[[File:Endo deriv4 summary.JPG]]

The C-C bond lengths formed are: 1.53574 and 1.53576 respectively.
Space distance between oxygen ad CH2-CH2 fragment: 1.53691


Space distance between oxygen ad CH2-CH2 fragment: 4.67325

The HOMO is of energy -0.38708 and is symmetric relative to the plane

[[File:Endo deriv4 HOMO.JPG|400px]]

The LUMO is of energy 0.01077 and is asymmetric relative to the plane


[[File:Endo_deriv4_LUMO.JPG|400px]]

The HOMO here has a node on the central oxygen atom and no apparent electron density on the other oxygens.

====EXO Form====

[[File:Exo freeze.log]]

[[File:EXO freeze.JPG|400px]]

Summary:

[[File:EXO_freeze_summary.JPG‎]]

The C-C bonds were then set to derivative.

[[File:Exo dirv.log]]

[[File:Exo dirv.JPG|400px]]

Summary:

[[File:EXO dirv summary.JPG]]

Partly Formed C-C Bond Lengths are: 1.53604 and 1.534603 respectively
Other Bond Lengths are : 1.53510

Space distance between oxygen ad CH2-CH2 fragment: 3.06650

HOMO symmetric with respect to plane and of energy:-0.38787

[[File:Exo HOMO.JPG|400px]]

LUMO asymmetric with respect to plane and of energy: 0.00602

[[File:EXO_LUMO.JPG|400px]]

In the HOMO, we can see that there a node on the atom and but there is bonding interactions along the top and bottom faces of the MO.

====Compare the endo and exo and discussion====

For the endo the energy is: -.160170084 a.u.
For the exo the energy is: -0.15990937 a.u.

From this we can see that the exo is higher in energy than the endo. This is because the reaction is supposed to be kinetically controlled. As such because the endo will be the more likely adduct for this reaction. The higher energy can be said to be due to the steric repulsions between the steric repulsions of the CH2-CH2 and Maleic and hydride. For the the endo, slightly lower energy as the pi interactions between the CH2-CH2 and -(C=O)-O-(C=O)- fragments have a secondary orbital interaction.

<ref name="Lazycat" />
From this we can conclude that steric effects have a larger effect on the energy of the structure than secondary overlap effect.


References

<references><ref name="LazyDog">http://en.wikipedia.org/wiki/Van_der_Waals_radius</ref>

<ref name="Lazycat">Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies, J. Org. Chem., 1987, 52 (8), pp 1469–1474</ref></references>