ChemWiki - User contributions [en]

Rep:Mod:mjf2310

2013-03-15T16:58:53Z

Mf2310: /* Activation Energies */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

{| class="wikitable" border="1"
|+
! colspan="11" style="text-align: Centre;"|Summary Energies
|-
| ||! colspan="5" style="text-align: Centre;"| '''HF/3-21G''' ||! colspan="5" style="text-align: Centre;"| '''B3LYP/6-31G*'''
|-
| ||'''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K''' || '''Activation Energy (au)''' / 298K ''(0K)'' || '''Activation Energy (kcal/mol)''' / 298K ''(0K)'' || '''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K'''|| '''Activation Energy (au)''' / 298K ''(0K) || '''Activation Energy (kcal/mol)''' / 298K ''(0K)
|-
| '''Chair TS''' || -231.61932148 || -231.466699 || -231.461340 || -0.071227 ''(-0.072841)'' || -44.69565477 ''(-45.70845591)'' || -234.55698243 || -234.414933 || -234.409008|| -0.052858 ''(-0.05428)'' || -33.16892358 ''(-34.0612428)''
|-
| '''Boat TS''' || -231.60280239 || -231.450928 || -231.445299
|| -0.087268 ''(-0.088612)'' || -54.76154268 ''(-55.60491612)'' || -234.5409304 || -234.402339 || -234.396005
|| -0.065861 ''(-0.066874)''|| -41.32843611 ''(-41.96410374)''
|-
| '''Hexadiene anti2''' || -231.69253529 || -231.539540 || -231.532567
|| - || - || -234.61171035 || -234.469213 || -234.461866 || - || -
|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:56:55Z

Mf2310: /* Activation Energies */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

{| class="wikitable" border="1"
|+
! colspan="11" style="text-align: Centre;"|Summary Energies
|-
| ||! colspan="5" style="text-align: Centre;"| '''HF/3-21G''' ||! colspan="5" style="text-align: Centre;"| '''B3LYP/6-31G*'''
|-
| ||'''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K''' || '''Activation Energy (au)''' / 298K ''(0K)'' || '''Activation Energy (kcal/mol)''' / 298K ''(0K)'' || '''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K'''|| '''Activation Energy (au)''' / 298K ''(0K) || '''Activation Energy (kcal/mol)''' / 298K ''(0K)
|-
| '''Chair TS''' || -231.61932148 || -231.466699 || -231.461340 || -0.071227 (-0.072841) || -44.69565477 (-45.70845591) || -234.55698243 || -234.414933 || -234.409008|| -0.052858 (-0.05428) || -33.16892358 (-34.0612428)
|-
| '''Boat TS''' || -231.60280239 || -231.450928 || -231.445299
|| -0.087268 (-0.088612) || -54.76154268 (-55.60491612) || -234.5409304 || -234.402339 || -234.396005
|| -0.065861 (-0.066874)|| -41.32843611 (-41.96410374)
|-
| '''Hexadiene anti2''' || -231.69253529 || -231.539540 || -231.532567
|| - || - || -234.61171035 || -234.469213 || -234.461866 || - || -
|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:56:03Z

Mf2310: /* Activation Energies */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

{| class="wikitable" border="1"
|+
! colspan="11" style="text-align: Centre;"|Summary Energies
|-
| ||! colspan="5" style="text-align: Centre;"| '''HF/3-21G''' ||! colspan="5" style="text-align: Centre;"| '''B3LYP/6-31G*'''
|-
| ||'''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K''' || '''Activation Energy (au)''' / 298K ''(0K)'' || '''Activation Energy (kcal/mol)''' / 298K ''(0K)'' || '''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K'''|| '''Activation Energy (au)''' / 298K ''(0K) || '''Activation Energy (kcal/mol)''' / 298K ''(0K)
|-
| '''Chair TS''' || -231.61932148 || -231.466699 || -231.461340
|| -0.071227 (-0.072841) || -44.69565477
(-45.70845591) || -234.55698243 || -234.414933 || -234.409008
|| -0.052858 (-0.05428) || -33.16892358 (-34.0612428)
|-
| '''Boat TS''' || -231.60280239 || -231.450928 || -231.445299
|| -0.087268 (-0.088612) || -54.76154268 (-55.60491612) || -234.5409304 || -234.402339 || -234.396005
|| -0.065861 (-0.066874)|| -41.32843611 (-41.96410374)
|-
| '''Hexadiene anti2''' || -231.69253529 || -231.539540 || -231.532567
|| - || - || -234.61171035 || -234.469213 || -234.461866 || - || -
|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:42:26Z

Mf2310: /* Activation Energies */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

{| class="wikitable" border="1"
|+
! colspan="11" style="text-align: Centre;"|Summary Energies
|-
| ||! colspan="5" style="text-align: Centre;"| '''HF/3-21G''' ||! colspan="5" style="text-align: Centre;"| '''B3LYP/6-31G*'''
|-
| ||'''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K''' || '''Activation Energy (au)''' / 298K ''(0K)'' || '''Activation Energy (kcal/mol)''' / 298K ''(0K)'' || '''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K'''|| '''Activation Energy (au)''' / 298K ''(0K) || '''Activation Energy (kcal/mol)''' / 298K ''(0K)
|-
| '''Chair TS''' || -231.61932148 || -231.466699 || -231.461340
|| || || -234.55698243 || -234.414933 || -234.409008
|| ||
|-
| '''Boat TS''' || -231.60280239 || -231.450928 || -231.445299
|| || || -234.5409304 || -234.402339 || -234.396005
|| ||
|-
| '''Hexadiene anti2''' || -231.69253529 || -231.539540 || -231.532567
|| - || - || -234.61171035 || -234.469213 || -234.461866 || - || -
|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:34:15Z

Mf2310: /* Activation Energies */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

{| class="wikitable" border="1"
|+
! colspan="11" style="text-align: Centre;"|Summary Energies
|-
| ||! colspan="5" style="text-align: Centre;"| '''HF/3-21G''' ||! colspan="5" style="text-align: Centre;"| '''B3LYP/6-31G*'''
|-
| ||'''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K''' || '''Activation Energy (au)''' / 298K ''(0K)'' || '''Activation Energy (kcal/mol)''' / 298K ''(0K)'' || '''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K'''|| '''Activation Energy (au)''' / 298K ''(0K) || '''Activation Energy (kcal/mol)''' / 298K ''(0K)
|-
| '''Chair TS''' || -231.61932148 || || || || || -234.55698243 || || || ||
|-
| '''Boat TS''' || -231.60280239 || || || || || -234.5409304 || || || ||
|-
| '''Hexadiene anti2''' || -231.69253529 || -231.539540 || -231.532567
|| || || -234.61171035 || -234.469213 || -234.461866 || ||
|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:27:50Z

Mf2310: /* Activation Energies */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

{| class="wikitable" border="1"
|+
! colspan="11" style="text-align: Centre;"|Summary Energies
|-
| ||! colspan="5" style="text-align: Centre;"| '''HF/3-21G''' ||! colspan="5" style="text-align: Centre;"| '''B3LYP/6-31G*'''
|-
| ||'''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K''' || '''Activation Energy (au)''' / 298K ''(0K)'' || '''Activation Energy (kcal/mol)''' / 298K ''(0K)'' || '''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K'''|| '''Activation Energy (au)''' / 298K ''(0K) || '''Activation Energy (kcal/mol)''' / 298K ''(0K)
|-
| '''Chair TS''' || -231.61932148 || || || || || -234.55698243 || || || ||
|-
| '''Boat TS''' || -231.60280239 || || || || || -234.5409304 || || || ||
|-
| '''Hexadiene anti2''' || -231.69253529 || || || || || -234.61171035 || || || ||
|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:23:22Z

Mf2310: /* Activation Energies */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

{| class="wikitable" border="1"
|+
! colspan="11" style="text-align: Centre;"|Summary Energies
|-
| ||! colspan="5" style="text-align: Centre;"| '''HF/3-21G''' ||! colspan="5" style="text-align: Centre;"| '''B3LYP/6-31G*'''
|-
| ||'''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K''' || '''Activation Energy (au)''' / 298K ''(0K)'' || '''Activation Energy (kcal/mol)''' / 298K ''(0K)'' || '''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K'''|| '''Activation Energy (au)''' / 298K ''(0K) || '''Activation Energy (kcal/mol)''' / 298K ''(0K)
|-
| '''Chair TS''' || -231.619322 || -231.466699 || -231.461341 || || || -234.556983 || -234.414933 || -234.409011|| ||
|-
| '''Boat TS''' || -231.602802 || -231.450933 || -231.445304 || || || -234.54309288 || -234.402336 || -234.396002|| ||
|-
| '''Hexadiene anti2''' || -231.692535 || -231.539539 || -231.532565 || || || -234.623175 || -234.481083 || -234.473723|| ||
|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:22:47Z

Mf2310: /* Activation Energies */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

{| class="wikitable" border="1"
|+
! colspan="7" style="text-align: Centre;"|Summary Energies
|-
| ||! colspan="5" style="text-align: Centre;"| '''HF/3-21G''' ||! colspan="5" style="text-align: Centre;"| '''B3LYP/6-31G*'''
|-
| ||'''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K''' || '''Activation Energy (au)''' / 298K ''(0K)'' || '''Activation Energy (kcal/mol)''' / 298K ''(0K)'' || '''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)/ 0K''' || '''Sum of electronic and thermal energies (au)/ 298K'''|| '''Activation Energy (au)''' / 298K ''(0K) || '''Activation Energy (kcal/mol)''' / 298K ''(0K)
|-
| '''Chair TS''' || -231.619322 || -231.466699 || -231.461341 || || || -234.556983 || -234.414933 || -234.409011|| ||
|-
| '''Boat TS''' || -231.602802 || -231.450933 || -231.445304 || || || -234.54309288 || -234.402336 || -234.396002|| ||
|-
| '''Hexadiene anti2''' || -231.692535 || -231.539539 || -231.532565 || || || -234.623175 || -234.481083 || -234.473723|| ||
|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:20:37Z

Mf2310: /* Activation Energies */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

{| class="wikitable" border="1"
|+
! colspan="7" style="text-align: Centre;"|Summary Energies
|-
| ||! colspan="3" style="text-align: Centre;"| '''HF/3-21G''' ||! colspan="3" style="text-align: Centre;"| '''B3LYP/6-31G*'''
|-
| ||'''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)''' || '''Sum of electronic and thermal energies (au)''' || '''Activation Energy''' (au) / 298K ''(0K) || '''Activation Energy (kcal/mol)''' / 298K ''(0K) || '''Electronic Energy (au)''' || '''Sum of electronic and zero-point energies (au)''' || '''Sum of electronic and thermal energies (au)'''
|-
| '''Chair TS''' || -231.619322 || -231.466699 || -231.461341 || || || -234.556983 || -234.414933 || -234.409011
|-
| '''Boat TS''' || -231.602802 || -231.450933 || -231.445304 || || || -234.54309288 || -234.402336 || -234.396002
|-
| '''Hexadiene anti2''' || -231.692535 || -231.539539 || -231.532565 || || || -234.623175 || -234.481083 || -234.473723
|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:12:09Z

Mf2310: /* Diels-Alder Cycloaddition */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:11:52Z

Mf2310: /* Diels-Alder Cycloaddition */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:11:28Z

Mf2310: /* Diels-Alder Cycloaddition */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

File:Transition states.jpg

2013-03-15T16:08:28Z

Mf2310:

Rep:Mod:mjf2310

2013-03-15T16:08:19Z

Mf2310: /* Introduction */

==Cope Rearrangement==
===Introduction===

The cope rearrangement is a [3+3] sigmatropic reaction in a 1,5-diene. The transition state for this reaction either resembles the chair conformer of cyclohexane or the boat conformer. Both of these structures are shown in the image below.

[[image:transition_states.jpg|thumb|centre|Possible Transition Structures for the Cope Rearrangement|300px]]

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T16:03:31Z

Mf2310: /* Diels-Alder Cycloaddition */

==Cope Rearrangement==
===Introduction===

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

The diels-alder reaction is a [4+2] concerted cycloaddition between a diene and a dienophile. For the reaction to be allowed the reactants must be symmetric which ensures that the orbital overlap between the diene and dienophile is sufficient.

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

File:BUTADIENE OPT2.jpg

2013-03-15T16:00:16Z

Mf2310:

Rep:Mod:mjf2310

2013-03-15T15:59:52Z

Mf2310: /* Butadiene and Ethylene */

==Cope Rearrangement==
===Introduction===

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BUTADIENE_OPT2.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T15:58:27Z

Mf2310: /* Activation Energies */

==Cope Rearrangement==
===Introduction===

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T15:57:04Z

Mf2310: /* Discussion */

==Cope Rearrangement==
===Introduction===

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present. The apparent absence of the secondary orbital effect is an example of the power of computational chemistry in challenging theories attempting to rationalise regioselectivity and relative energies of transition states.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

File:Hexadiene anti.jpg

2013-03-15T15:54:45Z

Mf2310:

File:Hexadiene gauche.jpg

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File:Hexadiene ci.jpg

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File:HEXADIENE CI 631G OPT2.jpg

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File:Hexadiene ci freq.jpg

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File:Chair 1st.jpg

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File:Chair 2nd.jpg

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File:CHAIR TS 3RD OPT5.jpg

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File:BOAT OPTFREQ FAIL2.jpg

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File:BOAT OPTFREQ8.jpg

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File:Chair 1st irc structure.jpg

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File:Chair 1st irc structure2.jpg

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File:CHAIR TS 631G2 FREQ.jpg

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File:BOAT OPT631G FREQ.jpg

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Rep:Mod:mjf2310

2013-03-15T15:51:45Z

Mf2310: /* Cope Rearrangement */

==Cope Rearrangement==
===Introduction===

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:HEXADIENE_CI_631G_FREQ6.LOG|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_2nd.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_3RD_OPT5.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ_FAIL2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPTFREQ8.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:chair_1st_irc_structure2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:CHAIR_TS_631G2_FREQ|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:BOAT_OPT631G_FREQ.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

File:HEXADIENE CI 631G FREQ6.LOG

2013-03-15T15:39:26Z

Mf2310:

Rep:Mod:mjf2310

2013-03-15T15:38:55Z

Mf2310: /* Cope Rearrangement */

==Cope Rearrangement==
===Introduction===

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_anti.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_gauche.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:HEXADIENE_CI_631G_OPT2.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:hexadiene_ci_freq.jpg|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T15:33:04Z

Mf2310: /* Cope Rearrangement */

==Cope Rearrangement==
===Introduction===

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T15:32:42Z

Mf2310: /* Introduction */

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T15:29:04Z

Mf2310: /* Discussion */

==Introduction==

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

However, from examination of the HOMO of the endo transition state, the interaction between the pi systems is out of phase and there is therefore nodal plane between the two fragments which suggests the secondary orbital effect is not present.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T15:20:46Z

Mf2310: /* Discussion */

==Introduction==

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi systems, which are not involved in bonding, of the cyclohexadiene and the maleic anhydride. This is demonstrated in the image below.

[[image:Secondary_orbital_effect.jpg|thumb|centre|Secondary Orbital Effect|300px]]

From examination of the nodal plane between the two fragments in the endo transition state, it appears that the secondary orbital effect is not present.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

File:Secondary orbital effect.jpg

2013-03-15T15:19:20Z

Mf2310:

Rep:Mod:mjf2310

2013-03-15T15:19:02Z

Mf2310: /* Discussion */

==Introduction==

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

Another possible explanation for the endo transition state being lower in energy is the secondary orbital effect. The secondary orbital effect is the favourable interaction between the pi system of the cyclohexadiene and the

From examination of the nodal plane between the two fragments in the endo transition state, it appears that the secondary orbital effect is not present.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T15:06:20Z

Mf2310: /* Discussion */

==Introduction==

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therefore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are broken/made simultaneously in one step.

One possible explanation for the regioselectivity observed is the steric hindrance experienced in the exo form between the O=C-O-C=O region of the maleic anhydride and the sp3 carbons of the cyclohexadiene. This steric hindrance prevents the two fragments from interacting at the optimal distance for maximal valence orbital overlap. The inter-fragment distance calculated and shown in the table above, validates this argument.

From examination of the nodal plane between the two fragments in the endo transition state, it appears that the secondary orbital effect is not present.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T15:01:53Z

Mf2310: /* Transition State */

==Introduction==

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || 2.29045 || 2.26831
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therfore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are borken/made simultaneously in one step.

From examination of the nodal plane between the two fragments in the endo transition state, it appears that the secondary orbital effect is not present.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T15:00:46Z

Mf2310: /* Transition State */

==Introduction==

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''Inter-fragment Distance (angstroms)''' || ||
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therfore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are borken/made simultaneously in one step.

From examination of the nodal plane between the two fragments in the endo transition state, it appears that the secondary orbital effect is not present.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T14:58:14Z

Mf2310: /* References */

==Introduction==

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therfore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are borken/made simultaneously in one step.

From examination of the nodal plane between the two fragments in the endo transition state, it appears that the secondary orbital effect is not present.

===References===

<references>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T14:58:04Z

Mf2310: /* Discussion */

==Introduction==

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therfore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are borken/made simultaneously in one step.

From examination of the nodal plane between the two fragments in the endo transition state, it appears that the secondary orbital effect is not present.

===References===

<ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244</references>

Rep:Mod:mjf2310

2013-03-15T14:57:02Z

Mf2310: /* Transition State */

==Introduction==

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Discussion====

Literature reports experimental formation of the endo product in 99% yield <ref>R. Gleiter, M. C. Bohm, ''Pure & Appl.Chem.'', 1983, '''55''', 237—244 </ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therfore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are borken/made simultaneously in one step.

From examination of the nodal plane between the two fragments in the endo transition state, it appears that the secondary orbital effect is not present.

Rep:Mod:mjf2310

2013-03-15T14:53:26Z

Mf2310: /* Transition State */

==Introduction==

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Transition State====

Literature reports experimental formation of the endo product in 99% yield <ref></ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therfore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control. Furthermore, the animation of the vibrational modes of each transition state confirm that the reaction is concerted and all bonds are borken/made simultaneously in one step.

From examination of the nodal plane between the two fragments in the endo transition state, it appears that the secondary orbital effect is not present.

Rep:Mod:mjf2310

2013-03-15T14:52:15Z

Mf2310: /* Transition State */

==Introduction==

==Cope Rearrangement==

===1,5 ''anti'' Hexadiene===

The ''anti'' conformer of Hexadiene was optimised at the HF/3-21G level. The completed optimisation file can be found on this [[media:HEXADIENE_ANTI_OPT12.LOG|link]]. From the symmetry point group and the total energy of the molecule, it is clear that the conformer that has been optimised is the ''anti1'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''anti'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69260233
|-
| '''RMS Gradient (au) ''' || 0.00001518
|-
| '''Dipole Moment (Debye)''' || 0.2020
|-
| '''Point Group''' || C2
|-
|}

===1,5 ''gauche'' Hexadiene===

Optimisation was performed on a molecule of 1,5- hexadiene with a 'Gauche' type linkage, using the same basis set as the 'anti' conformer. The completed file can be found on this [[media:HEXADIENE_GAUCHE_OPT4.LOG‎|link]]. The point group and the total energy of the molecule indicate that the optimised is the ''gauche2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - ''gauche'' Hexadiene Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69166702
|-
| '''RMS Gradient (au) ''' || 0.00000605
|-
| '''Dipole Moment (Debye)''' || 0.3806
|-
| '''Point Group''' || C2
|-
|}

===1,5- Hexadiene (Ci)===

====Optimisation (HF/3-21G)====
A 1,5-Hexadiene molecule with Ci symmetry was then constructed and optimised at the HF/3-21G level. The completed file can be found on this [[media:HEXADIENE_CI_OPT4.LOG|link]]. The total energy corresponds with the ''anti2'' conformer.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69253529
|-
| '''RMS Gradient (au) ''' || 0.00000666
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-
| '''Point Group''' || Ci
|-
|}

====Optimisation (DFT/6-31G*)====

The same molecule was then optimised at the DFT/6-31G* level. The completed file can be found on this [[media:HEXADIENE_CI_631G_OPT2.LOG|link]]

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Optimisation of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171035
|-
| '''RMS Gradient (au) ''' || 0.00001363
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

The basis set used in this optimisation is more accurate than the HF/3-21G basis set, which is why data between the two optimisations cannot be compared. However, geomtries of the optimised structures can be compared and since the 6-31G* basis set is more accurate, it is expected that the resulting geometry of the molecule will be more accurate. A table of the bond lengths and bond angles of the carbon chains of both optimised structures is shown below.

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Lengths (angstroms)
|-
| '''Bond''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2''' || 1.33352 || 1.31615
|-
| '''C2 - C3'''|| 1.50421 || 1.50891
|-
| '''C3 - C4'''|| 1.54808 || 1.55287
|-
| '''C4 - C5'''|| 1.50421 || 1.50889
|-
| '''C5 - C6'''|| 1.33352 || 1.31615
|-
|}

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"|1, 5 Hexadiene Ci Bond Angles (°)
|-
| '''Angle''' || '''6-31G*''' ||'''3-21G'''
|-
| '''C1 - C2 - C3 ''' || 125.3 || 124.8
|-
| '''C2 - C3 - C4'''|| 112.7 || 111.4
|-
| '''C3 - C4 - C5'''|| 112.7 || 111.4
|-
| '''C4 - C5 - C6'''|| 125.3 || 124.8
|-

|}

====Frequency Analysis (DFT/6-31G*)====

Frequency analysis was then performed on the optimised molecule, using the same basis set. The completed file can be found on this [[media:|link]]

The low frequencies below show that the conformer structure is at an energy minimum and that there are no negative frequencies present.

<pre>
Low frequencies --- -0.0012 -0.0008 -0.0007 1.2945 3.1483 9.3754
Low frequencies --- 73.8320 80.7551 120.9284
</pre>

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Frequency Analysis of 1,5 - Hexadiene (Ci) Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(D)
|-
| '''Final Energy (au)''' || -234.61171162
|-
| '''RMS Gradient (au) ''' || 0.00002150
|-
| '''Dipole Moment (Debye)''' || 0.000
|-
| '''Point Group''' || Ci
|-
|}

A list of energies, (in au), taken from the .log file is shown below.

<pre>
Sum of electronic and zero-point Energies= -234.469213
Sum of electronic and thermal Energies= -234.461866
Sum of electronic and thermal Enthalpies= -234.460922
Sum of electronic and thermal Free Energies= -234.500797
</pre>

===Optimisation of Chair Transition State===

All the following optimisation were performed at the HF/3-21G level of accuracy.

====1st Optimisation====

The transition structure was first optimised by using the Opt+Freq method, with optimisation to a transition structure (Berny), in Gaussview. The completed file can be found on this [[media:CHAIR_TS_1STOPT3.LOG|link]]. The job ran successfully as is demonstrated by the animation of the vibration at -817.90 cm-1, which is as expected for the Cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932244
|-
| '''RMS Gradient (au) ''' || 0.00002143
|-
| '''Dipole Moment (Debye)''' || 0.0008
|-

|}

[[image:Chair_ts_freq_animation.gif|thumb|centre|Animation of vibrational mode found at -817.90 cm-1 for Chair Transition Structure|300px]]

====2nd Optimisation====

Starting with the same input file as the 1st optimisation, a second optimisation was run using the frozen coordinate method. This method freezes the terminal carbons in place and optimises the transition structure around them. The completed file can be found on this [[media:CHAIR_TS_2NDOPT.LOG|link]]. The distance between the two terminal carbon atoms was fixed at 2.29431 and 2.22066 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61310641
|-
| '''RMS Gradient (au) ''' || 0.00490312
|-
| '''Dipole Moment (Debye)''' || 0.0053
|-

|}

====3rd Optimisation====

Using the structure from the second optimisation, a third optimisation was performed with the coordinates of the terminal carbons unfrozen, which enabled the distance between the terminal carbons to be optimised rather than fixed at 2.2 angstroms. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT5.LOG|link]]. The distance between the terminal carbons was found to be 2.02038 and 2.01905 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 3rd Optimisation of Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932148
|-
| '''RMS Gradient (au) ''' || 0.00010616
|-
| '''Dipole Moment (Debye)''' || 0.0004
|-

|}

===Optimisation of Boat Transition State===

The boat transition state was then optimised using the QST2 method. The first calculation performed was an opt+freq job type, with the optimisation to a QST2 rather than a TS (Berny), as was calculated previously. The completed optimisation log file can be found on this [[media:BOAT_OPTFREQ_FAIL2.LOG|link]]. From looking at the image from the checkpoint file of the optimised structure, (shown in results table below), it appears the calculation has failed since the transition state shown resembles a chair transition state rather than a boat transition state.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.61932229
|-
| '''RMS Gradient (au) ''' || 0.00003990
|-
| '''Dipole Moment (Debye)''' || 0.0007
|-

|}

The geometry of the input molecule was then modified such that the structures were closer to that of the boat transition state. This was achieved by setting the central dihedral angle to 0° and the angle at the two ends of the chain was set to 100°. The optimisation was then run using the same method as above and the image of the checkpoint file below shows that the optimisation yielded a boat transition structure. The completed optimisation file can be found on this [[media:BOAT_OPTFREQ8.LOG|link]]. The low frequencies shown below confirm that there is only one imaginary frequency which corresponds to the cope rearrangement.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Optimisation of Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60280239
|-
| '''RMS Gradient (au) ''' || 0.00003613
|-
| '''Dipole Moment (Debye)''' || 0.1583
|-

|}

<pre>
Low frequencies --- -840.0247 -3.4691 -3.1288 -0.0011 -0.0007 -0.0007
Low frequencies --- 2.4309 155.2101 381.8906
****** 1 imaginary frequencies (negative Signs) ******
</pre>

[[image:Boat_animation.gif|thumb|center|Animation of Boat Transition State Motion|300px]]

===Intrinsic Reaction Coordinate===

In order to accurately determine which product confomer is formed from the transition structures optimised previously, the Intrinsic Reaction Coordinate, (IRC), method was employed. Using this method, Gaussian follows the minimum energy path along the reaction coordinate and makes a series of small changes in geometry of the transition state in the direction where the gradient of the potential energy surface is the steepest. The resulting file shows a series of different structures and the structure with the minimum energy corresponds to the product of the reaction and hence can be used to determine which conformer is formed from the transition state.

The IRC was performed on the chair transition state, which was optimised previously as described above. The first IRC method was performed with 44 steps and the force constant was calculated at each step. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC.LOG|link]]. Each step corresponds to a different strucutre and shown below is a summary of the results, a plot of the IRC path and an image of the lowest energy structure.

[[file:Chair_1st_IRC.jpg|800px]]

[[image:Chair_1st_mininmum_IRC.jpg|thumb|left|Lowest Energy Structure|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 1st Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69157855
|-
| '''RMS Gradient (au) ''' || 0.00015231
|-
| '''Dipole Moment (Debye)''' || 0.3630
|-

|}

From the Root Mean Squared gradient graph it is clear that the lowest energy structure, (shown in image below: number 44), is not at a minimum as the RMS plot is still decreasing and has not flattened out. Therefore the IRC was run again, this time with 200 steps. The completed file can be found on this [[media:CHAIR_TS_3RD_OPT_IRC2.LOG|link]]. Although 200 steps were specified only 44 steps were yielded from the calculation since the structure at the 43rd step corresponds to the minimum energy structure. The 43rd step, (circled), in the RMS plot is clearly the minimum energy structure. An image of the lowest energy structure, (step 43), is shown below as well as the data for this structure. From the data supplied in the appendix it can be concluded that this structure is conformer '''gauche4'''. Therefore the conformer that results from the chair transition state is '''gauche4'''.

[[file:chair_2nd_IRC.jpg|800px]]

[[image:chair_2nd_minimum_IRC.jpg|thumb|left|Lowest Energy Structure from 2nd IRC (gauche4)|300px]]
{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| 2nd Lowest Energy Structure Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .chk
|-
| '''Calculation Type''' || IRC
|-
| '''Calculation Method''' ||
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.69153000
|-
| '''RMS Gradient (au) ''' || 0.00006942
|-
| '''Dipole Moment (Debye)''' ||
|-

|}

===Activation Energies===

In order to calculate and compare the activation energies of the chair and boat transition states, both optimised molecules must first be reoptimised at the higher level of accuracy, DFT/6-31G*.

The 3rd optimised chair file was used and reoptimised at this higher level. The completed file can be found on this [[media:CHAIR_TS_631G2.LOG|link]] and the 'item' from the log file, is shown below.

<pre>

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000750 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-2.106536D-07
Optimization completed.
-- Stationary point found.

</pre>

Frequency analysis was then performed on the optimised structure. The completed file can be found on this [[media:CHAIR_TS_631G2_FREQ.LOG|link]] and a table of results is shown below.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Chair Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.55698243
|-
| '''RMS Gradient (au) ''' || 0.00007978
|-
| '''Dipole Moment (Debye)''' || 0.0001
|-

|}

The same process was performed on the boat transition state. Firstly, it was optimised at the DFT/6-31G* level, the completed file can be found on this [[media:BOAT_OPT631G_3.LOG|link]], then a frequency analysis was performed on it, which can be found on this [[media:BOAT_OPT631G_FREQ.LOG|link]].

<pre>

Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000719 0.001800 YES
RMS Displacement 0.000173 0.001200 YES
Predicted change in Energy=-3.499470D-08
Optimization completed.
-- Stationary point found.
</pre>

TABLE OF ACTIVATION ENERGIES!!!!!!

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Reoptimised Boat Transition State Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31G(d)
|-
| '''Final Energy (au)''' || -234.5409304
|-
| '''RMS Gradient (au) ''' || 0.00000854
|-
| '''Dipole Moment (Debye)''' || 0.0614
|-

|}

==Diels-Alder Cycloaddition==

===Introduction===

===Butadiene and Ethylene===

A molecule of cis-butadiene was optimised at the semi-empirical AM1 level. The completed file can be found on this [[media:BUTADIENE_OPT2.LOG|link]]. Below is an image of the HOMO and LUMO of the optimised structure.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Final Energy (au)''' || 0.04879719
|-
| '''RMS Gradient (au) ''' || 0.00001745
|-
| '''Dipole Moment (Debye)''' || 0.0414
|-

|}

[[image:Butadiene_HOMO.jpg|thumb|centre|cis-Butadiene HOMO|300px]]
[[image:Butadiene_LUMO.jpg|thumb|centre|cis-Butadiene LUMO|300px]]

From the images above, it can be seen that the HOMO is antisymmetric with regards to the plane perpendicular to the plane of the molecule, and the LUMO is symmetric in relation to the same plane.

====Transition State====

To optimise the transition state, the frozen coordinate method was employed. The interfragment distance was set to 2.2 angstroms and the rest of the molecule was optimised to a transition state at the HF/3-21G level of accuracy. Following this the interfragment distance was then optimised. The completed file can be found on this [[media:DIELS_ALDER_TS_OPT2_2.LOG|link]]. Shown below is the input file, a summary of the results and an image of the optimised transition state.

The optimised inter-fragment distance was found to be 2.20294 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| cis-Butadiene and Ethylene Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:1st_TS.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -231.60320842
|-
| '''RMS Gradient (au) ''' || 0.00005589
|-
| '''Dipole Moment (Debye)''' || 0.5753
|-

|}

Frequency analysis was then performed on the optimised transition state to confirm the presence of only 1 imaginary frequency, (at -818.0 cm-1). The completed file can be found on this [[media:DIELS_ALDER_TS_FREQ2.LOG|link]]. An image of the motion of this vibrational mode is shown below. The animation below confirms that the transition state characterised is for the Diels-Alder reaction.

[[image:Diels_alder_1st.gif|thumb|centre|Animation of the imaginary vibrational mode of cis-Butadiene and Ethylene Transition State|300px]]

[[image:1st_TS_HOMO_nodal.jpg|thumb|left|Transition State HOMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State HOMO|300px]]

[[image:1st_TS_LUMO_nodal.jpg|thumb|left|Transition State LUMO|300px]][[image:1st_TS_HOMO_symmetry.jpg|thumb|right|Transition State LUMO|300px]]

===Cyclohexadiene and Maleic Anhydride===

A molecule of cyclohexadiene was optimised at the HF/3-21G level, the completed file can be found on this [[media:CYCLOHEXADIENE_OPT_321G2.LOG|link]]. A molecule of maleic anhydride was then optimised using the same basis set, the completed file can be found on this [[media:MALEIC_ANHYDRIDE_321G2.LOG|link]].

====Transition State====

The two optimised molecules were arranged so that the interfragment distance was 2.2 angstroms, an optimisation to a TS(Berny) and a frequency analysis was then performed on this molecule at the HF/321G level/. The exo form was optimised first, using the SCAN and the completed file can be found on this [[media:ENDO_TS4.LOG|link]]. The low frequencies data extracted from the .log file shows that there is only one imaginary frequency which confirms the presence of a transition state. The animation of the 1 imaginary vibrational frequency of the exo form is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Exo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:Exo_actual_ts.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.60359124
|-
| '''RMS Gradient (au) ''' || 0.00001151
|-
| '''Dipole Moment (Debye)''' || 5.9367
|-

|}

<pre>
Low frequencies --- -647.4729 -2.2892 -0.8256 -0.0009 -0.0008 -0.0006
Low frequencies --- 1.6264 42.3320 131.3858
****** 1 imaginary frequencies (negative Signs) ******
</pre>

The same procedure was then carried out on the endo form. The completed file can be found on this [[media:Log_74684.log|link]] and the file was also published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24362]. and an animation of the one imaginary frequency is shown in the table below. The optimised interfragment distance in the transition state was found to be 2.26065 angstroms.

Both of the transition states were then reoptimised, using the SCAN, at the higher level of accuracy of DFT/6-31G*. The exo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24363], and the completed file can be found on this [[media:log_74688.log|link]]. The endo transition state was published to D-space here [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/24364], and the completed file can be found on this [[media:log_74687.log|link]].

The reactants were then also reoptimised using the 6-31G basis set, in order to calculate more accurate activation energies. The completed cyclohexadiene file can be found on this [[media:CYCLOHEXADIENE_OPT_631G2.LOG|link]] and the completed maleic anhydride file can be found on this [[media:MALEIC_ANHYDRIDE_631G2.LOG|link]].

{| class="wikitable" border="1"
|+
! colspan="2" style="text-align: center;"| Endo Transition State Optimisation Data
|-
! colspan="2" style="text-align: Centre;"|[[File:endo_ts1.jpg|200px]]
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Final Energy (au)''' || -605.61036823
|-
| '''RMS Gradient (au) ''' ||0.00000004
|-
| '''Dipole Moment (Debye)''' || 6.7143
|-

|}

<pre>
Low frequencies --- -647.5215 -1.6910 -1.0853 0.0003 0.0004 0.0008
Low frequencies --- 0.4671 42.4426 131.4365
****** 1 imaginary frequencies (negative Signs) ******
</pre>

Shown below is a table of the data obtained from the opt+freq calculations carried out on the exo and endo transition state. The energies in italics represent the data obtained from the 3-21G basis set and the other energies are those obtained from the 6-31G* basis set. The activation energies were obtained from subtracting the energy of the transition state from the combined energies of the reactants, (maleic anhydride and cyclohexadiene).

{| class="wikitable" border="1"
|+
! colspan="3" style="text-align: Centre;"| Maleic Anhydride and Cyclohexadiene Diels-Alder Transition States
|-
! style="text-align: Centre;"| || Exo || Endo
|-
| style="text-align: Centre;"| '''Energy (au)''' /6-31G ''(3-21G)'' || -612.67931091 ''(-605.60359119)'' || -612.68339670 ''(-605.61036823)''
|-
| style="text-align: Centre;"| '''Imaginary Frequency Animation''' ||[[File:Exo_actual_ts.gif|200px]] || [[File:Endo_actual_ts.gif|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo1.jpg|200px]] || [[File:Endo_homo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO''' || [[File:Exo_homo2.jpg|200px]] || [[File:Endo_homo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''LUMO Energy (au)''' /6-31G || -0.07839 || -0.24229
|-
| style="text-align: Centre;"| '''LUMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo1.jpg|200px]] || [[File:Endo_lumo1.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO''' || [[File:Exo_lumo2.jpg|200px]] || [[File:Endo_lumo2.jpg|200px]]
|-
| style="text-align: Centre;"| '''HOMO Energy (au)''' /6-31G || -0.24216 || -0.06772
|-
| style="text-align: Centre;"| '''HOMO Symmetry''' || asymmetric || asymmetric
|-
| style="text-align: Centre;"| '''Activation Energy (au)''' /6-31G ''(3-21G)'' || -0.02611887 ''(-0.03959278)'' || -0.02203308 ''(-0.03281574)''
|-
| style="text-align: Centre;"| '''Activation Energy (kcal/mol)''' /6-31G ''(3-21G)'' || -16.3898521137 ''(-24.8448653778)'' || -13.8259780308 ''(-20.5922050074)''
|-
|}

====Transition State====

Literature reports experimental formation of the endo product in 99% yield <ref></ref>, and the data computed above shows that the endo transition state is the lowest in energy and has the smallest activation energy, therfore the first conclusion that can be made is that this particular diels-alder reaction proceeds under kinetic control.

From examination of the nodal plane between the two fragments in the endo transition state, it appears that the secondary orbital effect is not present.