Module 3

The Cope Rearrangement Tutorial

Optimizing the Reactants and Products

Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 180⁰) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.

%mem=10500MB
# opt hf/3-21g geom=connectivity

Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C₂. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1^[1] it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.

Fig. 1b Anti (1) 1,5-hexadiene Summary Table

Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene

Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 60⁰). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C₁. By comparing these values with those in appendix 1^[2] it is clear that the structure obtained from this optimisation is the gauche (3).

Fig. 1d Gauche (3) 1,5-hexadiene Summary Table

Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.

Fig. 1e Steric clash between alkene groups

Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations

The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.

%mem=10500MB
# opt hf/3-21g geom=connectivity

Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.

%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity

Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G*

The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.

Distance between carbon atoms	Anti (2) HF/3-21G	Distance between carbon atoms	Anti (2) B3LYP/6-31G*
C₁₄-C₇	1.3161	C₁₄-C₇	1.3335
C₄-C₇	1.5089	C₇-C₄	1.5042
C₄-C₁	1.5528	C₄-C₁	1.5481
C₁-C₉	1.5089	C₁-C₉	1.5042
C₉-C₁₁	1.3161	C₉-C₁₁	1.3335

Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene

A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.

# freq b3lyp/6-31g(d) geom=connectivity

Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.

Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations

Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum

The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

Energy term	Energy @298.15K / (a.u.)	Energy @ 0K / (a.u.)	Difference
The sum of the electronic and zero-point energies	-234.469212	-234.468775	0.000437
The sum of electronic and thermal energies	-234.461856	-234.461429	0.000427
The sum of electronic and thermal enthalpies	-234.460912	-234.460485	0.000427
The sum of electronic and thermal free energies	-234.500821	-234.500372	0.000449

Optimizing the "Chair" and "Boat" Transition Structures

Part a: Drawing an allyl fragment (CH₂CHCH₂), optimising it and using it to then form a reasonably good starting structure for finding transition states

The allyl fragment (CH₂CHCH₂) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.

Fig. 1a Optimised allyl fragment HF/3-21G

Fig. 1b Two allyl fragments: Chair transition state (guess)

Part b: Optimising the starting structure to a TS(Berny)

The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.

# opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity

The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm^-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.

Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths

Fig. 1d Chair transition state HF/3-21G: Imaginary vibration

Fig. 1e Chair transition state: Table of vibrations

Part c and d: Optimising the starting structure using the frozen coordinate method

The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.

# opt=modredundant hf/3-21g geom=connectivity

Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.

# opt=(ts,modredundant) rhf/3-21g geom=connectivity

The optimised structure is shown below.

Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths

Part e: Optimising the boat transition structure

The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.

# opt=qst2 freq hf/3-21g geom=connectivity

This calculation failed (DOI:10042/to-4183 ). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.

Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail

Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work

This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm^-1.

Fig. 1i Boat transition state TS(QST2): Imaginary vibration

Part f: Intrinsic Reaction Coordinate calculation

The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5. The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.

# irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck

This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.

# opt rhf/3-21g geom=connectivity

# irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity

Graph showing how the total energy changes IRC N=50

Graph showing how the gradient of the PES changes IRC N=50

Graph showing how the total energy changes IRC Calculating force constants at every step

Graph showing how the gradient of the PES changes IRC Calculating force constants at every step

Part g: Calculating activation energies

The Diels Alder Cycloaddition

Part a: Drawing and optimising Cis butadiene

A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method. The top line of the .gjf input file for this calculation is given below.

# opt am1 geom=connectivity

Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b. The HOMO is anti-symmetric and the LUMO is symmetric.

Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway

Fig. 1e Transition state: Imaginary vibration

Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo

Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclohexa-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.

# opt freq am1 geom=connectivity

Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.

Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride with Cyclohexa-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms on the opposite -CH₂-CH₂-/ -CH=CH- fragment of the diene.

Fig. 1j Endo transition state: Distances between atoms

Fig. 1l Exo transition state: Distances between atoms

Distance between carbon atoms	Endo Transition State	Distance between carbons atoms	Exo Transition State
C₁₇-C₄	2.89194	C₁₇-C₁₂	2.94501
C₁₅-C₁	2.89287	C₁₅-C₉	2.94498
C₂₀-C₃	2.16193	C₂₀-C₂	2.1703
C₂₂-C₂	2.1628	C₂₂-C₃	2.17035

Figures. 1k and 1m are animations of the one imaginary frequency of each transition state. For the endo transition state this was at -806cm^-1 and for the exo transition state this was at -812cm^-1.

Fig. 1k Endo transition state: Imaginary vibration

Fig. 1m Exo transition state: Imaginary vibration

The table below gives the relative energy of the exo and endo transition state calculated using three different semi empirical approximations. Regardless of which approximation was used the energy of the endo transition state was higher than that of the exo transition state. This was quite unexpected since the reaction is kinectically controlled. To help understand why the energy of the endo transition state is higher than the energy of the exo transition state the molecular orbitals of each transition state were analysed.

'	Endo transition state	Exo transition state
AMI	-0.05150453	-0.05041982
DFT	-612.4954778	-612.4909815
MP2	-610.8362244	-610.8308724

The table below shows the HOMO and LUMO of the endo and exo transition states generated using three different semi empirical approximations.

'	ENDO TRANSITION STATE	'	EXO TRANSITION STATE	'
AM1	Endo transition state HOMO AM1	Endo transition state LUMO AM1	Exo transition state HOMO AM1	Exo transition state LUMO AM1
DFT	Endo transition state HOMO DFT	Endo transition state LUMO DFT	Exo transition state HOMO DFT	Exo transition state LUMO DFT
MP2	Endo transition state HOMO MP2	Endo transition state LUMO MP2	Exo transition state HOMO MP2	Exo transition state LUMO MP2

References

[1] ttp://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3

[2] ttp://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3

[1]

[2]