File:Soo exo.jpg

2009-12-22T17:16:53Z

Azr07:

File:Soo exo.tiff

2009-12-22T17:15:42Z

Azr07:

Rep:Complab3:zeya1989

2009-12-22T17:01:48Z

Azr07: /* iii) */

==Module Introduction ==
In this set of computational experiments, the transition structures will be characterised on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. The transition state structures will be located based on the local shape of a potential energy surface, using orbital-based methods, numerically solving the Schrodinger equation. All calculations in this module were carried out on Gaussian 09W and then visualised in GaussView 3.0 and/or GaussView 5.0, as well as occasional use of ChemBio3D 12.0 Ultra.

General Note on Accuracy and Convention
*total energies are reported in atomic unit of Hartree (E'h').
*relative energies are reported in KJ/mol, and are only valid for systems with identical number and type of atoms.
*the energy calculate has an error of ≈ 10 kJ/mol, which is equivalent of 0.00381 Hartree(1E''h'' = 2625.5 kJ/mol)
*the dipole moment is accurate to about 2 decimal places, ie 0.01 Debye.
*frequencies in wavenumbers are by convention reported to the nearest whole integer with stematic error of around 10%.
*intensities are reported with no dedimal places by convention although accuracy is much less than this.
*bond distances are accurate to ≈ 0.01 Å
*bond angles are accurate to ≈ 0.1°
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
 
----

===The Cope Rearrangement===

The Cope Rearrangement is an example of a [3,3]-sigmatropic shift rearrangement, and is generally accepted that the reaction occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure higher in energy. In this tutorial we will show how Gaussian calculations of enthalpies and activation energies are in good agreement with the experimental values .
[[Image:Azr07_cope.gif|frame|Fig. 1 - The Cope Rearrangement]]

====Optimising the Reactants and Products====
The 10 most stable conformations of 1,5-hexdiene are shown in [[Mod:phys3#Appendix 1|Appendix 1]]. It is vital to characterise the conformers since higher energy conformers may stifle the rearrangement. A series of calculations are carried out below to optimise the structures on Gaussian.

=====a)=====
The two vinyl groups are manually altered so that they are not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle is set to 180.0°, and then the C3-C4-C5-C6 dihedral angle is set to -109.0 so that the vinyl groups appear to be further apart.

The command for the optimisation is as follows:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/3/32/Azr07_react_anti_log.txt azr07_react_anti.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/c/c6/Azr07_react_anti_rs.txt azr07_react_anti_rs.txt]
 
[[Image:Azr07_react_anti.jpg|thumb|500px|left|Conformer1]]
 
After symmetrising the structure a Ci{E,i} symmetry is achieved. Conformer 1 has energy of -231.69254 a.u.
 

=====b)=====
A fresh 'gauche' structure is drawn on Gaussvie with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°. The energy of this conformer is expected to be higher than conformer 1 as shown above, since the methylene hydrogens are synperiplanar to the vinyl hydrogens in the gauche form, producign steric strain.

Here is the optimisation command:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/d/dd/Azr07_react_gauche_log.txt azr07_react_gauche.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/0/07/Azr07_react_gauche_rs.txt azr07_react_gauche_rs.txt]
 
[[Image:Azr07_react_gauche.jpg|thumb|500px|left|Conformer 2]]
 
This gauche form is indeed higher in energy at -231.69153 a.u compared to the previous conformer. Conformer 2 has a C2 symmetry.
 

=====c)=====
To create the lowest energy conformation, the dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar.

This structure is subjected to the optimisation:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/8/83/Azr07_react_anti_b_log.txt azr07_react_anti_b.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/c/c4/Azr07_react_anti_b_rs.txt azr07_react_anti_b_rs.txt]
 
[[Image:Azr07_react_anti_b.JPG|thumb|500px|left|Conformer 3]]
 
Conformer 3 has energy of -231.69260 a.u and is lower in energy (approx 3 KJ/mol) than conformer 1, it is indeed more stable. The symmetrized structure belongs to the C2{E,C2} point group.
 

=====d)=====
From energy and structural comparisons, the above conformers correspond to the labeled equivalents [[Mod:phys3#Appendix 1|here]] as follows:

*Conformer 1 is equivalent to ''anti2'' with energy at -231.69254 a.u.
*Conformer 2 is equivalent to ''gauche4'' with energy at -231.69153 a.u.
*Conformer 3 is equivalent to ''anti1'' with energy at -231.69260 a.u.
 

=====e)=====
The ''anti2'' conformation has already been calculated in sectin a). as conformer 1.

=====f)=====
Previous minisation of conformer 1 successfully calculated the energy of the structure to a good agreement with that of the ''anti2'' structure. This is then reoptimised using a higher level basis set in order to achieve a better estimate of the conformer.

Conformer 1 is subjected to a DFT-B3LYP/6-31G(d) optimisation:
<pre>
# opt b3lyp/6-31g(d) geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/f/f2/Azr07_react_anti_ex_log.txt azr07_react_anti_ex.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/3/3d/Azr07_react_anti_ex_rs.txt azr07_react_anti_ex_rs.txt]

Overall the geometry changes are too small to make any visual impact. Table 1 summarises the details of the minor differences in the geometries.

{|border="1"
|-
!colspan="6"|Table 1 - Geometry parameters of ''Conformer 1''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31
|align="right"|1.33
!C1-C2-C3-C4 / °
|align="right"|-114.6
|align="right"|-118.6
|-
!C2-C3 / Å
|align="right"|1.51
|align="right"|1.50
!C2-C3-C4-C5 / °
|align="right"|-180.0
|align="right"|180.0
|-
!C3-C4 / Å
|align="right"|1.55
|align="right"|1.55
!C3-C4-C5-C6 / °
|align="right"|114.7
|align="right"|118.6
|-
!C4-C5 / Å
|align="right"|1.51
|align="right"|1.50
|-
!C5-C6 / Å
|align="right"|1.32
|align="right"|1.33
|}
 

=====g)=====
Conformer 1 is subjected to a frequency analysis via the following command:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/1/16/Azr07_react_anti_freq_log.txt azr07_react_anti_freq.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/8/8e/Azr07_react_anti_freq_rs.txt azr07_react_anti_freq.txt]

No imaginary frequencies are observed; the ananlysis is also fully converged. Below is the data extracted from the Thermochemistry section in the output file:

* Sum of electronic and zero-point energies:-234.46920 a.u.
* Sum of electronic and thermal energies: -234.46186 a.u.
* Sum of electronic and thermal enthalpies: -234.46091 a.u.
* Sum of electronic and free energies: -234.50078 a.u.
 
----

====Optimising the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) is drawn in GaussView and optimised using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity
0 2
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/f/f5/Azr07_allyl_opt_log.txt azr07_allyl_opt.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/b/b4/Azr07_allyl_opt_rs.txt azr07_allyl_opt_rs.txt]

[[Image:Azr07_allylchair.jpg|thumb|400px|left|Fig. 2 - Chair arrangement of allyl fragments]]
 
The optimised allyl fragment is duplicated and the two fragments arranged to approximately 2.2 Å apart to resemble the chair conformation of the transition state.
 

=====b)=====
The chair approximation is subjected to optimisation and frequency analysis to the transition state with the additional keywords opt=noeigen:
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/e/e1/Azr07_chair_guess_optfreq_log.txt azr07_chair_optfreq.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/0/08/Azr07_chair_guess_optfreq_rs.txt azr07_chair_optfreq_rs.txt]
 
[[Image:Azr07_chair_guess_optfreq.jpg|thumb|300px|left|Optimised chair transition state via TS (Berny)]]
 
An imaginary frequency at -817 cm-1 is observed. Further study of the vibrations at this frequency proves that this is where the bond-forming/bond-breaking takes place in the Cope rearrangement:
 
[[Image:Azr07_chair_guess_imagfreq.jpg|thumb|300px|left|Chair transition state vibration -817 cm-1]]
 
Symmetric vibration at terminal carbons at each fragment, however antiphase within each fragment. This leads to the sigmatropic shift.
 

=====c)=====
Now in order to make sure that the optimisation indeed leads to a transition state minimum rather than a different local minimum, the frozen coordinate method is used by selecting the 'Redundant Coord Editor' option. The terminal carbons from the allyl fragments which form/break a bond during the rearrangement are fixed at 2.2 Å apart, while the rest of the structure will be optimised to an energy minimum.

This is subjected to the following command for optimisation:
<pre>
# opt=modredundant hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/9/90/Azr07_chair_rce_opt_log.txt azr07_chair_rce.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/8/81/Azr07_chair_rce_opt_rs.txt azr07_chair_rce_rs.txt]
 
The optimised structure looks very much similar to the transition state achieved in b), except the bond forming/breaking distances are fixed to 2.2 Å.
 

=====d)=====
Now the transition state will be optimised without calculating the force constants. This requires using a normal guess Hessian modified to include the information about the two coordinates where bond breaking/forming takes place.

The optimisation is subjected to the following:

<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/4/44/Azr07_chair_rce2_opt_log.txt azr07_chair_rce2.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/e/e1/Azr07_chair_rce2_opt_rs.txt rce_chair_rce2_rs.txt]
 
[[Image:Azr07_chair_rce2.JPG|thumb|300px|left|Optimised chair transition state via RCE]]
 
The output transition state resembles visually to that produced using the RCE method. To further compare the two structures the numerical differences are studied with regards to structural geometry in Table 2.
{|border="1"
|-
!colspan="3"|Table 2 - Parameter of chair transition state via RCE and Hessian
|-
!Parameter
!TS (Berny) Optimisation
!RCE Optimisation
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38
|align="right"|1.38
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01
|align="right"|2.02
|-
!align="right"|dihedral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9
|align="right"|54.9
|-
!align="right"|Energy / Eh
|align="right"|-231.61932
|align="right"|-231.61932
|}
 
As can be seen in Table 2, there are no significant numerical differences with regards to the structures. Both methods are successful in reaching the transition state structure.

=====e)=====
The QST2 method will be used for the boat structure optimisation. This method relies on translating portions of the reactant to yield the product, and stopping at the transition state. The HF/3-21G optimised ''anti2'' structure is duplicated in GaussView, maniputlated and renumbered as shown in Figure 3.
 
[[Image:Azr07_boat_input.JPG|thumb|500px|left|Fig. 3 - Reactant and product of ''anti2'']]
 
This is then subjected to the following:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/a/aa/Azr07_boat_qst_opt_fail.LOG azr07_boat_qst_fail.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/1/18/Azr07_boat_qst_opt_fail_rs.txt azr07_boat_qst_fail_rs.txt]
 
It is not a surprise that the calculation failed as the QST2 method did not rotate about any of the bonds, and thus explains the fact that the output structure looked like a more disassociated version of the chair transition state. To fix this the input structures are modified such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (originally 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°), as shown in Figure 4.
 
[[Image:Azr07_boat_input2.JPG|thumb|500px|left|Fig. 4 - Modified Reactant and product for boat structure]]
 
The calculation is run via the following command:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/2/22/Azr07_boat_qst_opt.LOG azr07_boat_qst.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/2/2e/Azr07_boat_qst_opt_rs.txt azr07_boat_qst.txt]
 
[[Image:Azr07_boat_opt.jpg|thumb|300px|left|Optimised boat transition state via QST2]]
 

=====f)=====
The boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformation, while the chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformation. To further prove this is indeed the case, an Intricsic Reaction Coordinate calculation is used for each conformer to find the geometric minimum starting from the transition state.
It is noted that the initial IRC calculation does not produce a minimum, and there are 3 options to fix this problem. I have decided to use the solution where the IRC is re-run but specifying that the force constants are computed at every step. The advantage of this method is that it is the most reliable.

Firstly the IRC calculation is excuted for the chair transition state, with a 50 step limit and force constants:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/4/4b/Azr07_chair_IRC50fc.LOG azr07_chair_IRC50fc.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/2/27/Azr07_chair_irc50fc_rs.txt azr07_chair_IRC50fc_rs.txt]
 
[[Image:Azr07_chair_irc50fc.jpg|thumb|300px|left|IRC output for chair transition state]]
 
The output corresponds to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer, both having the same energy too.
 

Secondly the same process is carried out for the boat transition state, with the following command:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/9/90/Azr07_boat_IRC50fc.LOG azr07_boat_IRC60fc.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/e/ec/Azr07_boat_irc50fc_rs.txt azr07_boat_IRC60fc_rs.txt]
 
[[Image:Azr07_boat_irc50fc.jpg|thumb|300px|left|IRC output structure for boat transition state]]
 
As predicted, the output structure resembles to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer.
 

=====g)=====
In order to make better comparisons between the activation energy for the Cope rearrangement, it is best to use energies derived from high-level optimisations; thus the chair and boat transition states are firstly optimised again at (DFT-B3LYP/6-31G(d)) level, followed by frequency analysis at the same level in order to produce the Thermochemistry data.

The chair transition state is subjected to the following for optimisation:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity
0 1
</pre>
Log file:[https://www.ch.imperial.ac.uk/wiki/images/6/63/Azr07_log_chair_reopt.txt azr07_chair_reopt.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/4/45/Azr07_chair_reopt_rs.txt azr07_chair_reopt_rs.txt]

The frequency analysis for the chair transition state is run via the following command:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity
0 1
</pre>
Log file:[https://www.ch.imperial.ac.uk/wiki/images/5/50/Azr07_log_chair_refreq.txt azr07_chair_refreq.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/9/9c/Azr07_chair_refreq_rs.txt azr07_chair_refreq_rs.txt]

For the boat transition state the same processes are repeated and the output files are attached as follows:

Reoptimisation log file: [https://www.ch.imperial.ac.uk/wiki/images/4/44/Azr07_log_boat_reopt.txt azr07_boat_reopt.LOG]
Reoptimisation results summary: [https://www.ch.imperial.ac.uk/wiki/images/6/61/Azr07_boat_reopt_rs.txt azr07_boat_reopt_rs.txt]

Frequency log file: [https://www.ch.imperial.ac.uk/wiki/images/6/62/Azr07_log_boat_refreq.txt azr07_boat_refreq.LOG]
Frequency results summary: [https://www.ch.imperial.ac.uk/wiki/images/d/de/Azr07_boat_refreq_rs.txt azr07_boat_refreq_rs.txt]

Table 3 and 4 below summarises the data from these calculations.

{| border="1" cellspacing="1" cellpadding="10"
|-
!colspan="7"|Table 3 - Energies of transition states and reactant in Hartree
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61953
| align="center" | -231.46670
| align="center" | -231.46134
| align="center" | -234.55493
| align="center" | -234.41400
| align="center" | -234.40780
|-
| '''Boat TS'''
| align="center" | -231.60280
| align="center" | -231.45093
| align="center" | -231.44530
| align="center" | -234.54309
| align="center" | -234.40234
| align="center" | -234.39600
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253
| align="center" | -231.53953
| align="center" | -231.53256
| align="center" | -234.61171
| align="center" | -234.46920
| align="center" | -234.46186
|}

 

{| border="1" cellspacing="1" cellpadding="10"
|-
!colspan="6"|Table 4 - Summary of activation energies (in kcal/mol)
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.54
| align="center" | 44.77
| align="center" | 32.65
| align="center" | 33.21
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.62
| align="center" | 54.66
| align="center" | 41.88
| align="center" | 41.34
| align="center" | 44.7 ± 2.0
|}

 

From the above data it is straightforward to conclude that it is more favourable if the Cope rearrangement proceeds via the chair transition state, as this conformation has the lower energy and minimal steric strain.

----

===The Diels Alder Cycloaddition===
The Diels Alder reaction belongs to a class of reactions known as pericyclic reactions, and are commonly held to be concerted processes. The π orbitals of the dieneophile are used to form new σ bonds with the π orbitals of the diene - this will be proved in this exercise.

The first reaction is the Diels-Alder reaction between ethylene and cis-butadiene.

=====i)=====
Cis-butadiene is drawn in GaussView and optimised via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/4/4e/Azr07_cisbut.LOG azr07_cisbut.LOG]

The molecular orbitals are examined so to understand the feasibility of this reaction. It is expected that the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. Orbitals can be labeled as either symmetric '''s''' or antisymmetric '''a''' with respect to the reflection plane, and only orbitals with the same symmetry are able to interact during an reaction. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below.
 
{|align="center"
|-
|[[Image:Azr07_ethene_homo.jpg|thumb|220px|Ethene HOMO '''s''']]
|[[Image:Azr07_ethene_lumo.jpg|thumb|220px|Ethene LUMO '''a''']]
|[[Image:Azr07_cisbut_homo.jpg|thumb|220px|Cis-butadiene HOMO '''a''']]
|[[Image:Azr07_cisbut_lumo.jpg|thumb|220px|Cis-butadiene LUMO '''s''']]
|}
 
It can be seen that the HOMOs are of different symmetries, as are the LUMOs. Therefore the interaction can only occur across the HOMO/LUMO pair. The HOMO of ethylene and the LUMO of butadiene are both '''s''' and the LUMO of ethylene and the HOMO of butadiene are both '''a'''. Energetically, the HOMO of the resulting adduct with two new σ bonds is '''a''', indicating a stronger interaction between Ethene HOMO and Cis-butadiene LUMO.

=====ii)=====
QST3 method is chosen to determine the transition state for this prototype reaction. Prior to optimisation, three structures are drawn in GaussView, namely cis-butadiene, ethene and the transition state and cyclohexene and arranged spacially as shown in Figure 5 to imply an angled trajectory.
[[Image:Azr07_tsguess.JPG|thumb|left|600px|Fig. 5 - reactants (left), product (middle) and guess at transition state (right)]]
 
The command code for this QST3 optimisation is as follows:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/9/9f/Azr07_tsguess.LOG azr07_ts_guess.LOG]

The reaction is a thermal π4s + π2s cycloaddition, proceeding via a Hückel transition state, and is symmetry allowed.
 
[[Image:Azr07_ts_homo.jpg|thumb|220px|left|Transition state HOMO]]
 
The HOMO is of symmetry '''a''', which as previously shown, is formed by interaction between the HOMO of cis-butadiene and LUMO of ethene.
 
As on would expect the C(H2)-C(H) bond lengths are indeed longer than their equivalents in cis-butadiene, being 1.38 Å on average; the C2-C3 bond shows increases in bond order, being a more C=C-reminiscent 1.39 Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are both 2.11 Å and hence makes the transition state symmetrical, i.e. both bonds are formed simultaneously. The partially formed σ-bonds are less than double the Van der Waals radius(1.9 A for Carbon)<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>.
 

An imaginary frequency is observed, which correspond to the bond vibration for the partial σ-bonds at -956 cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds. The lowest positive frequency is observed at 147 cm-1. This vibration is asymmetric and includes a torsional component about the ethene portion.
{|align="centre"
|-
|[[Image:Azr07_ts_opt.jpg|thumb|280px|Optimised transition state]]
|[[Image:Azr07_ts_imafreq.jpg|thumb|280px|Transition state vibration at -956 cm-1]]
|[[Image:Azr07_ts_lowposfreq.jpg|thumb|280px|Transition state vibration 147 cm-1]]
|}
 

=====iii)=====
[[Image:Azr07_iii_rxnscheme.png|thumb|550px|left|Fig. 6 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]
The Diels Alder reaction between cyclohexa-1,3-diene and maleic anhydride is more complicated the previous example, as there are two possible products, the exo '''3''' and the endo '''4''' product. The approach of reaction for each isomer is different, and therefore QST3 is employed to determine the transition state for each path.

The reactants and products firstly drawn in ChemBio3D and then imported into GaussView. Each was optimised via the AM1 semi-empirical method.

The exo and endo transition states are both determined via the following command individually:

<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity
0 1
</pre>
Exo log file: [https://www.ch.imperial.ac.uk/wiki/images/0/0a/Azr07_ts_exo_opt.LOG azr07_exo_ts_opt.LOG]
Endo log file: [https://www.ch.imperial.ac.uk/wiki/images/a/a4/Azr07_ts_endo_opt.LOG azr07_endo_ts_opt.LOG]

{|align="left"
|-
|[[Image:Azr07_ts_exo.jpg|thumb|250px|Exo transition state]]
|[[Image:Nm607_endo_transition_state.jpg|thumb|250px|Endo transition state]]
|}
 
The exo isomer has higher energy than the endo isomer, -0.05042 a.u. vs -0.05150 a.u. Structurally, the exo isomer is more strained than than the endo, as it is destabilised more due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Azr07_sterics.gif|thumb|600px|left|Fig. 7 - Steric interactions in the exo and endo transition states]]
 
Following the same procedure used in the previous exercise, in order to understand the MOs of the transition states, the MOs of the reactants are firstly examined.

{|align="centre"
|-
|[[Image:Azr07_cyclohexadiene_homo.jpg|thumb|200px|Cyclohexadiene HOMO '''a''']]
|[[Image:Azr07_cyclohexadiene_lumo.jpg|thumb|200px|Cyclohexadiene LUMO '''s''']]
|[[Image:Azr07_maleicanhydride_homo.jpg|thumb|200px|Maleic anhydride HOMO '''s''']]
|[[Image:Azr07_maleicanhydride_lumo.jpg|thumb|200px|Maleic anhydride LUMO '''a''']]
|}
The HOMO of cyclohexadiene and LUMO of maleic anydride interacts more strongly than the other pair, because the anhydride group is a strong electron-withdrawing group, and therefore prefers donation from the HOMO of cyclohexadiene into its LUMO. This HOMO/LUMO interaction forms the HOMO of both transition state structures.
 
{|align="centre"
|-
|[[Image:Azr07_ts_exo_homo.jpg|thumb|200px|Exo HOMO '''a''']]
|[[Image:Azr07_ts_exo_lumo.jpg|thumb|200px|Exo LUMO '''a''']]
|[[Image:Azr07_ts_endo_homo.jpg|thumb|200px|Endo HOMO '''a''']]
|[[Image:Azr07_ts_endo_lumo.jpg|thumb|200px|Endo LUMO '''a''']]
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----

Rep:Complab3:zeya1989

2009-12-22T16:59:54Z

File:Azr07 maleicanhydride lumo.jpg

2009-12-22T16:50:11Z

Azr07:

File:Azr07 maleicanhydride homo.jpg

2009-12-22T16:49:58Z

Azr07:

File:Azr07 cyclohexadiene lumo.jpg

2009-12-22T16:49:15Z

Azr07:

Azr07:

File:Azr07 ts exo.jpg

2009-12-22T16:15:39Z

Azr07:

File:Azr07 ts exo opt.LOG

2009-12-22T16:14:36Z

Azr07:

2009-12-22T15:48:26Z

Azr07: /* ii) */

==Module Introduction ==
In this set of computational experiments, the transition structures will be characterised on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. The transition state structures will be located based on the local shape of a potential energy surface, using orbital-based methods, numerically solving the Schrodinger equation. All calculations in this module were carried out on Gaussian 09W and then visualised in GaussView 3.0 and/or GaussView 5.0, as well as occasional use of ChemBio3D 12.0 Ultra.

General Note on Accuracy and Convention
*total energies are reported in atomic unit of Hartree (E'h').
*relative energies are reported in KJ/mol, and are only valid for systems with identical number and type of atoms.
*the energy calculate has an error of ≈ 10 kJ/mol, which is equivalent of 0.00381 Hartree(1E''h'' = 2625.5 kJ/mol)
*the dipole moment is accurate to about 2 decimal places, ie 0.01 Debye.
*frequencies in wavenumbers are by convention reported to the nearest whole integer with stematic error of around 10%.
*intensities are reported with no dedimal places by convention although accuracy is much less than this.
*bond distances are accurate to ≈ 0.01 Å
*bond angles are accurate to ≈ 0.1°
*1 Hartree unit (Eh) = 2625.5 kJ mol-1 = 627.51 kcal mol-1
 
----

===The Cope Rearrangement===

The Cope Rearrangement is an example of a [3,3]-sigmatropic shift rearrangement, and is generally accepted that the reaction occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure higher in energy. In this tutorial we will show how Gaussian calculations of enthalpies and activation energies are in good agreement with the experimental values .
[[Image:Azr07_cope.gif|frame|Fig. 1 - The Cope Rearrangement]]

====Optimising the Reactants and Products====
The 10 most stable conformations of 1,5-hexdiene are shown in [[Mod:phys3#Appendix 1|Appendix 1]]. It is vital to characterise the conformers since higher energy conformers may stifle the rearrangement. A series of calculations are carried out below to optimise the structures on Gaussian.

=====a)=====
The two vinyl groups are manually altered so that they are not on the same side of the C3-C4 bond, reducing their steric repulsion. To make this structure the C2-C3-C4-C5 dihedral angle is set to 180.0°, and then the C3-C4-C5-C6 dihedral angle is set to -109.0 so that the vinyl groups appear to be further apart.

The command for the optimisation is as follows:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/3/32/Azr07_react_anti_log.txt azr07_react_anti.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/c/c6/Azr07_react_anti_rs.txt azr07_react_anti_rs.txt]
 
[[Image:Azr07_react_anti.jpg|thumb|500px|left|Conformer1]]
 
After symmetrising the structure a Ci{E,i} symmetry is achieved. Conformer 1 has energy of -231.69254 a.u.
 

=====b)=====
A fresh 'gauche' structure is drawn on Gaussvie with the C1-C2-C3-C4, C2-C3-C4-C5 and C3-C4-C5-C6 dihedral angles set at 60°. The energy of this conformer is expected to be higher than conformer 1 as shown above, since the methylene hydrogens are synperiplanar to the vinyl hydrogens in the gauche form, producign steric strain.

Here is the optimisation command:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/d/dd/Azr07_react_gauche_log.txt azr07_react_gauche.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/0/07/Azr07_react_gauche_rs.txt azr07_react_gauche_rs.txt]
 
[[Image:Azr07_react_gauche.jpg|thumb|500px|left|Conformer 2]]
 
This gauche form is indeed higher in energy at -231.69153 a.u compared to the previous conformer. Conformer 2 has a C2 symmetry.
 

=====c)=====
To create the lowest energy conformation, the dihedral angles between the three carbon-carbon bond pairs was altered to be 180° to make all carbon-carbon bonds antiperiplanar.

This structure is subjected to the optimisation:
<pre>
%mem=250MB
# opt hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/8/83/Azr07_react_anti_b_log.txt azr07_react_anti_b.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/c/c4/Azr07_react_anti_b_rs.txt azr07_react_anti_b_rs.txt]
 
[[Image:Azr07_react_anti_b.JPG|thumb|500px|left|Conformer 3]]
 
Conformer 3 has energy of -231.69260 a.u and is lower in energy (approx 3 KJ/mol) than conformer 1, it is indeed more stable. The symmetrized structure belongs to the C2{E,C2} point group.
 

=====d)=====
From energy and structural comparisons, the above conformers correspond to the labeled equivalents [[Mod:phys3#Appendix 1|here]] as follows:

*Conformer 1 is equivalent to ''anti2'' with energy at -231.69254 a.u.
*Conformer 2 is equivalent to ''gauche4'' with energy at -231.69153 a.u.
*Conformer 3 is equivalent to ''anti1'' with energy at -231.69260 a.u.
 

=====e)=====
The ''anti2'' conformation has already been calculated in sectin a). as conformer 1.

=====f)=====
Previous minisation of conformer 1 successfully calculated the energy of the structure to a good agreement with that of the ''anti2'' structure. This is then reoptimised using a higher level basis set in order to achieve a better estimate of the conformer.

Conformer 1 is subjected to a DFT-B3LYP/6-31G(d) optimisation:
<pre>
# opt b3lyp/6-31g(d) geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/f/f2/Azr07_react_anti_ex_log.txt azr07_react_anti_ex.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/3/3d/Azr07_react_anti_ex_rs.txt azr07_react_anti_ex_rs.txt]

Overall the geometry changes are too small to make any visual impact. Table 1 summarises the details of the minor differences in the geometries.

{|border="1"
|-
!colspan="6"|Table 1 - Geometry parameters of ''Conformer 1''
|-
!Bond Lengths
!HF/3-21G
!DFT-B3LYP/6-31G(d)
!Dihedral Angles
!HF/3-21G
!DFT-B3LYP/6-31G(d)
|-
!C1-C2 / Å
|align="right"|1.31
|align="right"|1.33
!C1-C2-C3-C4 / °
|align="right"|-114.6
|align="right"|-118.6
|-
!C2-C3 / Å
|align="right"|1.51
|align="right"|1.50
!C2-C3-C4-C5 / °
|align="right"|-180.0
|align="right"|180.0
|-
!C3-C4 / Å
|align="right"|1.55
|align="right"|1.55
!C3-C4-C5-C6 / °
|align="right"|114.7
|align="right"|118.6
|-
!C4-C5 / Å
|align="right"|1.51
|align="right"|1.50
|-
!C5-C6 / Å
|align="right"|1.32
|align="right"|1.33
|}
 

=====g)=====
Conformer 1 is subjected to a frequency analysis via the following command:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/1/16/Azr07_react_anti_freq_log.txt azr07_react_anti_freq.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/8/8e/Azr07_react_anti_freq_rs.txt azr07_react_anti_freq.txt]

No imaginary frequencies are observed; the ananlysis is also fully converged. Below is the data extracted from the Thermochemistry section in the output file:

* Sum of electronic and zero-point energies:-234.46920 a.u.
* Sum of electronic and thermal energies: -234.46186 a.u.
* Sum of electronic and thermal enthalpies: -234.46091 a.u.
* Sum of electronic and free energies: -234.50078 a.u.
 
----

====Optimising the "Chair" and "Boat" Transition Structures====
=====a)=====
An allyl fragment (CH2CHCH2) is drawn in GaussView and optimised using the HF/3-21G method:
<pre>
# opt hf/3-21g geom=connectivity
0 2
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/f/f5/Azr07_allyl_opt_log.txt azr07_allyl_opt.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/b/b4/Azr07_allyl_opt_rs.txt azr07_allyl_opt_rs.txt]

[[Image:Azr07_allylchair.jpg|thumb|400px|left|Fig. 2 - Chair arrangement of allyl fragments]]
 
The optimised allyl fragment is duplicated and the two fragments arranged to approximately 2.2 Å apart to resemble the chair conformation of the transition state.
 

=====b)=====
The chair approximation is subjected to optimisation and frequency analysis to the transition state with the additional keywords opt=noeigen:
<pre>
# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/e/e1/Azr07_chair_guess_optfreq_log.txt azr07_chair_optfreq.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/0/08/Azr07_chair_guess_optfreq_rs.txt azr07_chair_optfreq_rs.txt]
 
[[Image:Azr07_chair_guess_optfreq.jpg|thumb|300px|left|Optimised chair transition state via TS (Berny)]]
 
An imaginary frequency at -817 cm-1 is observed. Further study of the vibrations at this frequency proves that this is where the bond-forming/bond-breaking takes place in the Cope rearrangement:
 
[[Image:Azr07_chair_guess_imagfreq.jpg|thumb|300px|left|Chair transition state vibration -817 cm-1]]
 
Symmetric vibration at terminal carbons at each fragment, however antiphase within each fragment. This leads to the sigmatropic shift.
 

=====c)=====
Now in order to make sure that the optimisation indeed leads to a transition state minimum rather than a different local minimum, the frozen coordinate method is used by selecting the 'Redundant Coord Editor' option. The terminal carbons from the allyl fragments which form/break a bond during the rearrangement are fixed at 2.2 Å apart, while the rest of the structure will be optimised to an energy minimum.

This is subjected to the following command for optimisation:
<pre>
# opt=modredundant hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/9/90/Azr07_chair_rce_opt_log.txt azr07_chair_rce.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/8/81/Azr07_chair_rce_opt_rs.txt azr07_chair_rce_rs.txt]
 
The optimised structure looks very much similar to the transition state achieved in b), except the bond forming/breaking distances are fixed to 2.2 Å.
 

=====d)=====
Now the transition state will be optimised without calculating the force constants. This requires using a normal guess Hessian modified to include the information about the two coordinates where bond breaking/forming takes place.

The optimisation is subjected to the following:

<pre>
# opt=(ts,modredundant,noeigen) hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/4/44/Azr07_chair_rce2_opt_log.txt azr07_chair_rce2.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/e/e1/Azr07_chair_rce2_opt_rs.txt rce_chair_rce2_rs.txt]
 
[[Image:Azr07_chair_rce2.JPG|thumb|300px|left|Optimised chair transition state via RCE]]
 
The output transition state resembles visually to that produced using the RCE method. To further compare the two structures the numerical differences are studied with regards to structural geometry in Table 2.
{|border="1"
|-
!colspan="3"|Table 2 - Parameter of chair transition state via RCE and Hessian
|-
!Parameter
!TS (Berny) Optimisation
!RCE Optimisation
|-
!align="right"|C-C (allyl,avg.) / Å
|align="right"|1.38
|align="right"|1.38
|-
!align="right"|C-C (trans-allyl,avg.) / Å
|align="right"|2.01
|align="right"|2.02
|-
!align="right"|dihedral angle between tips of chair (abs(avg.)) / °
|align="right"|54.9
|align="right"|54.9
|-
!align="right"|Energy / Eh
|align="right"|-231.61932
|align="right"|-231.61932
|}
 
As can be seen in Table 2, there are no significant numerical differences with regards to the structures. Both methods are successful in reaching the transition state structure.

=====e)=====
The QST2 method will be used for the boat structure optimisation. This method relies on translating portions of the reactant to yield the product, and stopping at the transition state. The HF/3-21G optimised ''anti2'' structure is duplicated in GaussView, maniputlated and renumbered as shown in Figure 3.
 
[[Image:Azr07_boat_input.JPG|thumb|500px|left|Fig. 3 - Reactant and product of ''anti2'']]
 
This is then subjected to the following:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/a/aa/Azr07_boat_qst_opt_fail.LOG azr07_boat_qst_fail.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/1/18/Azr07_boat_qst_opt_fail_rs.txt azr07_boat_qst_fail_rs.txt]
 
It is not a surprise that the calculation failed as the QST2 method did not rotate about any of the bonds, and thus explains the fact that the output structure looked like a more disassociated version of the chair transition state. To fix this the input structures are modified such that the C2-C3-C4-C5 and C2-C1-C6-C5 dihedral angles, for reactant and product respectively, were 0° (originally 180°) and the C2-C3-C4 and C2-C1-C6, and C3-C4-C5 and C1-C6-C5 bond angles were 100° (originally ~110°), as shown in Figure 4.
 
[[Image:Azr07_boat_input2.JPG|thumb|500px|left|Fig. 4 - Modified Reactant and product for boat structure]]
 
The calculation is run via the following command:
<pre>
# opt=(qst2,noeigen) freq hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/2/22/Azr07_boat_qst_opt.LOG azr07_boat_qst.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/2/2e/Azr07_boat_qst_opt_rs.txt azr07_boat_qst.txt]
 
[[Image:Azr07_boat_opt.jpg|thumb|300px|left|Optimised boat transition state via QST2]]
 

=====f)=====
The boat transition state best resembles the [[Mod:phys3#Appendix 1|''gauche3'']] conformation, while the chair transition state best resembles the [[Mod:phys3#Appendix 1|''gauche2'']] conformation. To further prove this is indeed the case, an Intricsic Reaction Coordinate calculation is used for each conformer to find the geometric minimum starting from the transition state.
It is noted that the initial IRC calculation does not produce a minimum, and there are 3 options to fix this problem. I have decided to use the solution where the IRC is re-run but specifying that the force constants are computed at every step. The advantage of this method is that it is the most reliable.

Firstly the IRC calculation is excuted for the chair transition state, with a 50 step limit and force constants:
 
<pre>
# irc=(forward,maxpoints=50,calcall) hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/4/4b/Azr07_chair_IRC50fc.LOG azr07_chair_IRC50fc.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/2/27/Azr07_chair_irc50fc_rs.txt azr07_chair_IRC50fc_rs.txt]
 
[[Image:Azr07_chair_irc50fc.jpg|thumb|300px|left|IRC output for chair transition state]]
 
The output corresponds to the [[Mod:phys3#Appendix 1|''gauche2'']] conformer, both having the same energy too.
 

Secondly the same process is carried out for the boat transition state, with the following command:
<pre>
# irc=(forward,maxpoints=60,calcall) hf/3-21g geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/9/90/Azr07_boat_IRC50fc.LOG azr07_boat_IRC60fc.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/e/ec/Azr07_boat_irc50fc_rs.txt azr07_boat_IRC60fc_rs.txt]
 
[[Image:Azr07_boat_irc50fc.jpg|thumb|300px|left|IRC output structure for boat transition state]]
 
As predicted, the output structure resembles to the [[Mod:phys3#Appendix 1|''gauche3'']] conformer.
 

=====g)=====
In order to make better comparisons between the activation energy for the Cope rearrangement, it is best to use energies derived from high-level optimisations; thus the chair and boat transition states are firstly optimised again at (DFT-B3LYP/6-31G(d)) level, followed by frequency analysis at the same level in order to produce the Thermochemistry data.

The chair transition state is subjected to the following for optimisation:
<pre>
# opt=(ts,noeigen,modredundant) b3lyp/6-31g(d) geom=connectivity
0 1
</pre>
Log file:[https://www.ch.imperial.ac.uk/wiki/images/6/63/Azr07_log_chair_reopt.txt azr07_chair_reopt.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/4/45/Azr07_chair_reopt_rs.txt azr07_chair_reopt_rs.txt]

The frequency analysis for the chair transition state is run via the following command:
<pre>
# freq b3lyp/6-31g(d) geom=connectivity
0 1
</pre>
Log file:[https://www.ch.imperial.ac.uk/wiki/images/5/50/Azr07_log_chair_refreq.txt azr07_chair_refreq.LOG]
Results summary: [https://www.ch.imperial.ac.uk/wiki/images/9/9c/Azr07_chair_refreq_rs.txt azr07_chair_refreq_rs.txt]

For the boat transition state the same processes are repeated and the output files are attached as follows:

Reoptimisation log file: [https://www.ch.imperial.ac.uk/wiki/images/4/44/Azr07_log_boat_reopt.txt azr07_boat_reopt.LOG]
Reoptimisation results summary: [https://www.ch.imperial.ac.uk/wiki/images/6/61/Azr07_boat_reopt_rs.txt azr07_boat_reopt_rs.txt]

Frequency log file: [https://www.ch.imperial.ac.uk/wiki/images/6/62/Azr07_log_boat_refreq.txt azr07_boat_refreq.LOG]
Frequency results summary: [https://www.ch.imperial.ac.uk/wiki/images/d/de/Azr07_boat_refreq_rs.txt azr07_boat_refreq_rs.txt]

Table 3 and 4 below summarises the data from these calculations.

{| border="1" cellspacing="1" cellpadding="10"
|-
!colspan="7"|Table 3 - Energies of transition states and reactant in Hartree
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61953
| align="center" | -231.46670
| align="center" | -231.46134
| align="center" | -234.55493
| align="center" | -234.41400
| align="center" | -234.40780
|-
| '''Boat TS'''
| align="center" | -231.60280
| align="center" | -231.45093
| align="center" | -231.44530
| align="center" | -234.54309
| align="center" | -234.40234
| align="center" | -234.39600
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253
| align="center" | -231.53953
| align="center" | -231.53256
| align="center" | -234.61171
| align="center" | -234.46920
| align="center" | -234.46186
|}

 

{| border="1" cellspacing="1" cellpadding="10"
|-
!colspan="6"|Table 4 - Summary of activation energies (in kcal/mol)
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.54
| align="center" | 44.77
| align="center" | 32.65
| align="center" | 33.21
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.62
| align="center" | 54.66
| align="center" | 41.88
| align="center" | 41.34
| align="center" | 44.7 ± 2.0
|}

 

From the above data it is straightforward to conclude that it is more favourable if the Cope rearrangement proceeds via the chair transition state, as this conformation has the lower energy and minimal steric strain.

----

===The Diels Alder Cycloaddition===
The Diels Alder reaction belongs to a class of reactions known as pericyclic reactions, and are commonly held to be concerted processes. The π orbitals of the dieneophile are used to form new σ bonds with the π orbitals of the diene - this will be proved in this exercise.

The first reaction is the Diels-Alder reaction between ethylene and cis-butadiene.

=====i)=====
Cis-butadiene is drawn in GaussView and optimised via the semi-empirical AM1 method:
<pre>
# opt am1 geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/4/4e/Azr07_cisbut.LOG azr07_cisbut.LOG]

The molecular orbitals are examined so to understand the feasibility of this reaction. It is expected that the HOMO of the diene/dienophile interacting with the LUMO of the dienophile/diene to have the same symmetry. Orbitals can be labeled as either symmetric '''s''' or antisymmetric '''a''' with respect to the reflection plane, and only orbitals with the same symmetry are able to interact during an reaction. Thus the symmetries of the HOMOs and LUMOs of cis-butadiene and ethene are shown below.
 
{|align="center"
|-
|[[Image:Azr07_ethene_homo.jpg|thumb|220px|Ethene HOMO '''s''']]
|[[Image:Azr07_ethene_lumo.jpg|thumb|220px|Ethene LUMO '''a''']]
|[[Image:Azr07_cisbut_homo.jpg|thumb|220px|Cis-butadiene HOMO '''a''']]
|[[Image:Azr07_cisbut_lumo.jpg|thumb|220px|Cis-butadiene LUMO '''s''']]
|}
 
It can be seen that the HOMOs are of different symmetries, as are the LUMOs. Therefore the interaction can only occur across the HOMO/LUMO pair. The HOMO of ethylene and the LUMO of butadiene are both '''s''' and the LUMO of ethylene and the HOMO of butadiene are both '''a'''. Energetically, the HOMO of the resulting adduct with two new σ bonds is '''a''', indicating a stronger interaction between Ethene HOMO and Cis-butadiene LUMO.

=====ii)=====
QST3 method is chosen to determine the transition state for this prototype reaction. Prior to optimisation, three structures are drawn in GaussView, namely cis-butadiene, ethene and the transition state and cyclohexene and arranged spacially as shown in Figure 5 to imply an angled trajectory.
[[Image:Azr07_tsguess.JPG|thumb|left|600px|Fig. 5 - reactants (left), product (middle) and guess at transition state (right)]]
 
The command code for this QST3 optimisation is as follows:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity
0 1
</pre>
Log file: [https://www.ch.imperial.ac.uk/wiki/images/9/9f/Azr07_tsguess.LOG azr07_ts_guess.LOG]

The reaction is a thermal π4s + π2s cycloaddition, proceeding via a Hückel transition state, and is symmetry
 
[[Image:Azr07_ts_homo.jpg|thumb|220px|left|Transition state HOMO]]
 
The HOMO is of symmetry '''a''', which as previously shown, is formed by interaction between the HOMO of cis-butadiene and LUMO of ethene.
 
[[Image:Azr07_ts_opt.jpg|thumb|280px|left|Optimised transition state]]
 
As on would expect the C(H2)-C(H) bond lengths are indeed longer than their equivalents in cis-butadiene, being 1.38 Å on average; the C2-C3 bond shows increases in bond order, being a more C=C-reminiscent 1.39 Å (literature value for typical C=C bond: 1.34 Å<ref name="978-0-495-38713-8">J. C. Kotz, P. Treichel, ''Chemistry & Chemical Reactivity, Volume 2'', '''2008''', ''7th Edition'', 387. ISBN 978-0-495-38713-8</ref>). The C1-C6 and C4-C5 bond lengths are both 2.11 Å and hence makes the transition state symmetrical, i.e. both bonds are formed simultaneously. The partially formed σ-bonds are less than double the Van der Waals radius(1.9 A for Carbon)<ref name="978-0-028-25527-9">R. C. Smoot, R. G. Smith, J. Price, ''Merrill Chemistry'', '''1999''', 316. ISBN 978-0-028-25527-9</ref>.
 

An imaginary frequency is observed, which correspond to the bond vibration for the partial σ-bonds at -956 cm-1. The vibration shows the symmetric, concerted formation of the two new σ-bonds.
[[Image:Azr07_ts_imafreq.jpg|thumb|300px|left|Transition state vibration at -956 cm-1]]
 
The lowest positive frequency is observed at 147 cm-1. This vibration is asymmetric and includes a torsional component about the ethene portion.
[[Image:Azr07_ts_lowposfreq.jpg|thumb|300px|right|Transition state vibration 147 cm-1]]
 

=====iii)=====
[[Image:Nm607_reaction_scheme.gif|frame|right|Fig. 20 - Reaction of cyclohexa-1,3-diene with maleic anhydride]]Cyclohexa-1,3-diene reacts with maleic anhydride according to the same Diels Alder chemistry as seen with cis-butadiene and ethene. What is different about this new system is that the complexity of the reacting groups allows two different products: the endo and the exo product. The approach path for each isomer is different, and would be difficult to enforce using QST2. Thus the method of choice is QST3, which allows direct control over the proposed transition state.

The reactants and products were built in ChemBio3D, and imported into GaussView. Each was optimized via the AM1 semi-empirical method and used where necessary to construct the transition states. The QST3 method was used on both transition states, but it was significantly more problematic finding the transition state for the endo conformer: repeated QST3 cycles (substituting the output transition state as the guess in the next calculation) did not yield a suitable transition state; nor did optimizing using the freeze/optimize-to-minimum/un-freeze/optimize-to-transition-state process work. What was eventually done was a careful manual adjustment of the transition state to a sensible shape - adjustment of the bond lengths such that all C-C bonds undergoing a change in bond order were set at 1.44 Å (bond order ~1.5) save for the inter-fragment bonds which were set at 2.2 Å, and geometric rearragements such as adjusting the groups around the methynes such that they were equidistant.

The code for the final endo transition state optimization:
<pre>
# opt=(calcall,ts,noeigen) am1 geom=connectivity

endo transition state opt2 AM1

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/b/bf/NM607_ENDO_TRANSITION_STATE_OPT3.LOG NM607_ENDO_TRANSITION_STATE_OPT3.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/a/a7/Nm607_endo_transition_state_opt3_results_summary.txt Nm607_endo_transition_state_opt3_results_summary.txt]

[[Image:Nm607_endo_transition_state.jpg|frame|left|300px|Fig. 21 - Endo transition state]]
 
The exo transition state was determined directly from a sensibly laid-out guess at a transition state in a QST3 calculation:
<pre>
# opt=(calcall,qst3,noeigen) freq am1 geom=connectivity

Title Card Required

0 1
</pre>
:Log file: [https://www.ch.ic.ac.uk/wiki/images/e/e9/NM607_EXO_TRANSITION_STATE.LOG NM607_EXO_TRANSITION_STATE.LOG]
:Results summary: [https://www.ch.ic.ac.uk/wiki/images/c/c9/Nm607_exo_transition_state_results_summary.txt Nm607_exo_transition_state_results_summary.txt]

[[Image:Nm607_exo_transition_state.jpg|frame|left|300px|Fig. 22 - Exo transition state]]
 

The vibrations of each transition state were of the right character to suggest that the transitionstate had in fact been reached and both calculations converged. The endo transition state had a calculated imaginary frequency of -806(.39) cm-1:
 
[[Image:Nm607_endo_transition_state_vibration-806.jpg|frame|left|Fig. 23 - Endo imaginary vibration]]
 
Likewise the exo transition state had an imaginary vibration that displayed symultaneous formation of both σ-bonds:
 
[[Image:Nm607_exo_transition_state_vibration-812.jpg|frame|left|Fig. 24 - Exo imaginary vibration]]
 
Diels Alder chemistry is sensitive to molecular orbital overlap, prior to bonding so analysing the molecular orbitals of the trasition states is vital for an understanding of the reaction kinetics. To properly analyse the molecular orbitals of the transition states it is first necessary to examine the molecular orbitals of the reactants:
 
{|border="1"
|-
!colspan="4"|Table 9 - HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
|-
!colspan="2"|cyclo-1,3-diene
!colspan="2"|maleic anhydride
|-
!Orbital
!Symmetry
!Orbital
!Symmetry
|-
|[[Image:Nm607_cyclohexadiene_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|a<ref>Not technically, but the approximation is sufficient for the purpose of showing compatable orbitals</ref>
|[[Image:Nm607_maleicanhydride_HOMO.jpg|thumb|200px|HOMO]]
|align="center"|s
|-
|[[Image:Nm607_cyclohexadiene_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|s
|[[Image:Nm607_maleicanhydride_LUMO.jpg|thumb|200px|LUMO]]
|align="center"|a
|}
 
The anhydride group is a strong electron-withdrawing group, and favours donation into the LUMO of maleic anhydride over donation from the HOMO. Thus, the interaction between the LUMO of maleic anhydride and the HOMO of cyclohexadiene is strongest; it is these two orbitals that combine to form the HOMO of the transition state.
 
{|border="1"
|-
!colspan="4"|Table 10 - Molecular orbitals of the endo and exo transition states
|-
!colspan="2"|endo
!colspan="2"|exo
|-
!width="220"|Orbital
!width="50"|Symmetry
!width="220"|Orbital
!width="50"|Symmetry
|-
|[[Image:Nm607_endo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_endo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_HOMO.jpg|thumb|200px|HOMO]]
[[Image:Nm607_exo_transition_state_HOMO(side).jpg|thumb|200px|HOMO (side-view)]]
|align="center"|a
|-
|[[Image:Nm607_endo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_endo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|[[Image:Nm607_exo_transition_state_LUMO.jpg|thumb|200px|LUMO]]
[[Image:Nm607_exo_transition_state_LUMO(side).jpg|thumb|200px|LUMO (side-view)]]
|align="center"|a
|}

The nodal character of the HOMO of the endo is such that all the oxygen atoms in the anhydride functionality have nodes in their centres (and lobes above and below, similar to p-orbitals). The lobes of the central oxygen atom extend outward, toward the other two oxygen atoms, rather than upwards/downwards as the other oxygen atoms' lobes do. The same situation exists for the endo transition state but the blending between the lobes of the central oxygen and any others is visible at lower isovalues than for the endo transition state.

Looking at the energies of the two isomers one is lead to the conclusion that the endo product is the kinetic product (the endo transition state is 2.85 kJ mol-1 more stable), but the question is "why?": first of all there is the secondary orbital overlap effect:
 
[[Image:Nm607_seconary_orbital_interactions.gif|frame|left|Fig. 23 - Secondary orbital overlap in the endo but not the exo transition state]]
 
What is demonstrated in Fig. 23 is that the endo transition state is stabilized, relative to the exo transition state, through additional electron donation from the π-system of cyclohexa-1,3-diene into the orbitals of the electron-poor maleic anhydride. There is no extra bonding involved, so the stabilization is small, but the stabilization is sufficient to favour the endo over the exo product in a kinetically controlled reaction. In such reactions it is also often a case that steric considerations impact on the preferred product (kinetic or otherwise). In this case the exo transition state is destabilized more than the endo transition state due to repulsion between the anhydride group and the cyclohexadiene ring.
 
[[Image:Nm607_destabilization.gif|frame|left|Fig. 24 - Steric interactions between maleic anydride and cyclohexa-1,3-diene in the endo and exo transition states]]
 
These two effects are of similar magnitude, and can often balance one another to the point where careful analysis is required to determine which product is the kinetic product and which is the thermodynamic product<ref name="jo00384a016">M. A. Fox, R. Cardona, N. J. Kiwiet, ''J. Org. Chem.'', '''1987''', ''52'', 1469–1474. {{DOI|10.1021/jo00384a016}}</ref>. In this case they act in the same direction, to stabilize the endo transition state, and stabilize the endo product (AM1 optimizations of both products yielded a 0.69 kJ mol-1 gap between the two, favouring the endo product: [[https://www.ch.ic.ac.uk/wiki/images/f/f3/Nm607_endo_opt_results_summary.txt|endo log file]]; [[https://www.ch.ic.ac.uk/wiki/images/7/7f/Nm607_exo_opt_results_summary.txt|exo log file). This is what the raw data indicates but it would be foolish to assume that the results are entirely accurate given the closeness in energy between the isomers and their transition states; it is entirely possible that a more intensive analysis could reverse the relative energies. However, the endo transition state can be rationalized as being the more stable and therefore the conclusion is that the endo product is at the very least the kinetic product.
----