Rep:Mod:CHEM121500122000

Yr 3 Physical Computational Module

Sebastian Strudley

Part 1: The Cope Rearrangement

The Cope Rearrangement is a [3,3] sigmatropic rearrangement of 1,5-hexadiene. It is an example of a pericyclic reaction that undergoes a concerted, cyclic transition state. The reactant and product of the cope rearrangement are chemically identical.

There has been a large degree of study of the Cope Rearrangement. For example, in 1971 Hoffmann and Stohrer published a paper investigating a variety of rearrangements based on the Cope rearrangement.

Optimizing energies of 1,5-hexadiene

• 1,5-hexadiene with an anti linkage about the central four C atoms was optimized using the HF/3-21G level of theory. The resulting structure corresponded to the anti2 structure within [Appendix 1] of the experimental script. The symmetry of the structure, and its energy was obtained from the calculation.

• A further anti conformation (anti4) was obtained, but this was higher in energy than the previously found conformation.

• Conformational studies have previously been completed on 1,5-hexadiene. In 1994 calculations were reported at the MP2/6-31G* level which showed 'little energy difference between the anti and gauche conformations'. This result was found in this exercise, with only a few kcal / mol difference in energy between the conformations.

• The group also reported 10 distinguishable conformations, with a gauche conformer having the lowest in energy. Further to this they report that 'an attractive interaction may be present between the π orbital and the vinyl proton'. If the central four atoms in 1,5-hexadiene are modelled as butane, an antiperiplanar arrangement of these atoms (as in the anti conformations below) would be expected to be lowest in energy. Somewhat suprisingly, for 1,5-hexadiene the lowest conformation exists with a gauche orientation of the central 4 atoms. The stabilising interaction between a π orbital and vinyl protons mentioned above could explain this phenomenon.

Energies were optimized as below:

Theory: HF/3-21G

Method: Hartree Fock

Basis Set: 3-21G

Conformer	Geometry	Point Group	Energy (Hartrees)	Energy (kcal/mol)	Relative Energy (kcal/mol)	Log File
Anti2		Ci / C1	-231.69253	-145389.29	0.0816	File:Anti2 .LOG
Anti4		C1	-231.69097	-145388.31	1.0605	File:Anti4 .LOG
Guache2		C2 / C1	-231.69167	-145388.75	0.6212	File:Guache2 .LOG
Guache3		C1	-231.69266	-145389.37	0	File:Guache3 .LOG

The Anti2 conformation.

• The anti2 conformation was further analysed at a higher level of theory (B3LYP/6-31G*). The results were compared to those obtained from the earlier calculations. Also, an IR spectrum was simulated.

Comparison between the HF/3-21G and B3LYP/6-31G* levels of theory.

• Little change in geometry was observed between the two calculations, however there are significant differences in the energies predicted by the two levels of theory.

Theory	Geometry View 1	Geometry View 2	Point Group	Sum of electronic and thermal energies (Hartrees)	Log File
HF/3-21G			Ci/C1	-231.532566	File:Anti2 .LOG
B3LYP/6-31G*			Ci/C1	-234.461857	File:Anti2B3LYP .LOG

IR Data

• The results of the IR calculation showed only real vibration frequencies (i.e. none reported with negative values). This is expected, as the spectrum was calculated for a 'real' molecule rather than a transition state. Some of the vibrations have been animated and are shown below.

An animation of a vibration (v = 1537 cm-1)

The IR Spectrum of the anti2 conformation. B3LYP/6-31G* Level

An animation of a vibration (v = 1718 cm-1)

Thermochemical Data

• The thermochemistry data for the anti2 conformation at the B3LYP/6-31G* level of theory is shown below. The data was collected from this log file: File:Anti2B3LYP .LOG

Parameter Energy (Hartrees) Sum of electronic and zero-point Energies -234.469204 Sum of electronic and thermal Energies -234.461857 Sum of electronic and thermal Enthalpies -234.460913 Sum of electronic and thermal Free Energies -234.500776

Description Potential energy at 0 K (E = Eelec + ZPE) Energy at 298 K and P = 1 atm (E = E + Evib + Erot+ Etranslational) Correction for RT (H = E + RT) Entropic contribution to the free energy (G = H - TS)

Optimizing the chair and boat TS structures

(a) Allyl (CH₂CHCH₂) fragment optimization

• In GuassView, a 3 carbon fragment was drawn and optimised at the HF/3-21G level of theory.

The optimised allyl fragment structure.

(b) Optimising to a TS (Berny) for a chair TS.

• A chair TS was approximated by positing two of the allyl fragments previously optimised in (a) with the allylic ends at a distance of around 2.2 Å apart.
• The resulting structure was obtained. The IR spectrum, and an animation of the imaginary vibration (negative frequency) are shown below.

• The log file from the calculation is avaliable here. File:Partb .LOG

The optimised chair TS geometry for the cope rearrangement. The optimised chair TS geometry for the cope rearrangement.	Animated imaginary vibration with frequency 818 cm-1
IR spectrum for the Cope rearrangement via the chair TS

(c) Optimising the structure using the frozen coordinate method.

• This part was not attempted due to the recent update to the Guassian software - please see script.

(d) Freezing the forming bond lengths using the redundant coordinate editor

• An optimisation calculation was attempted by fixing the bond distances that are broken / made to 2.2 Å.
• The input file was set up as per the screenshots below.

A screenshot of the input criteria for Part D

A screenshot of the input criteria for Part D

Unfortunately when the output file was analysed, the bond lengths of the forming bonds (2.025 Å - see below) were the same as those obtained in part (b), indicating that the attempt to fix the bond forming lengths was not successful.

A screenshot of the input criteria for Part D

(e) Optimising the boat TS structure, using the QST2 method

• The anti2 conformation obtained from a calculation at the B3LYP/6-31G* level was used as a starting point.
• Care was taken to ensure the atom numbering was correct for reactant to product.

Atoms numbering for the calculation.

• A QST calculation using Opt + Freq and TS (Berny) was attempted. This calculation failed.

• A further calculation was run with modified conditions in order to locate the boat transition state. The following changes to both reactant and product molecules were stipulated to achieve this:
  • C2-C3-C4-C5 dihedral angle: 0°
  • C2-C3-C4 angle: 100°
  • C3-C4-C5 angle: 100°

Atoms numbering for the calculation.

The boat TS obtained from a calculation at the QST2 level.

The boat TS obtained from a calculation at the QST2 level.

• A single imaginary vibration (v = -840.1 cm^-1) was observed in the output file from the calculation. This vibration is animated below:

The vibration at 840 cm-1 animated.

• As the calculation was successful, it suggests that the reactants and products were close to the TS, achieved by the stipulations above.

(f) Intrinsic Reaction Coordinate Method An IRC calculation was completed: Direction: Forward Force Constant: Calculate always IRC Max: None Number of points along IRC: 50 An animation of the IRC calculation. An animation of the IRC What conformers of 1,5-hexadiene do you think the chair and boat TS connect? The chair TS appears to connect the guache3 conformers whilst the boat TS appears to connect the gauche2 conformers. The last structure obtained from the IRC is shown below. This structure is not a minimum energy state in the Cope rearrangement. The last structure from the first IRC calculation. The last structure from the first IRC calculation. A series of additional calculations / adaptions to the IRC method were attempted, in order to obtain the minimum geometry. These are shown below: 1. Running a minimization from the last point on the IRC The structure of the last calculated point on the IRC (shown below) was copied and was optimised at the B3LYP/6-31G* level of theory. The structure of the re-optimised last point on the IRC at the B3LYP/6-31G* level. The energy was minimsed to a value of -234.460967 Hartrees (Sum of electronic and thermal energies). File:OPTOFLASTOFIRCOPTFREQ.LOG This energy corresponds fairly well to that of -234.460913 found for the anti2 conformation of the reactant. The structure resembles that of the reactant or product for the cope rearrangement (as the structure is symmetrical these are essentially the same). In order to provide evidence that the structure obtained corresponded to the initial or end structures (the 'minima'), bond distances were measured in GuassView. The software does not automatically draw a bond between the atoms which are connected after the transition state. The value obtained is shown below, and was compared to that measured for the anti2 internal C-C bond distance (the bond formed from the TS). The 'new bond' formed when the last coordinate of the IRC is minimised. Distance = 1.54825 Å The internal bond distance in the anti2 conformation - the reactant or product for the Cope rearrangement. Distance = 1.54810 Å The two bond distances compare favourably. This suggests that after minimisation of the last point on the IRC, we have returned to either the reactant or product molecule. 2. Restart the IRC with a larger number of points The IRC was restarted, this time using a 70 points along the IRC. This calculation resulted in an error. Log file is available here:File:IRCCALC70STEP.LOG. 3. Calculating the force constants at each step When the IRC was calculated above, the force constants were calculated at each step anyway.

(g) Calculating the activation energy for the reaction using both transition states

The activation energies for the reaction were then calculated using both the chair and boat transition states at the B3LYP/6-31G* level of theory.

Summary of energies for calculations at different levels of theory (Hartrees)

	HF/3-21G			B3LYP/6-31G*
	Electronic energy	Sum of electronic and zero-point energies	Sum of electronic and thermal energies	Electronic energy	Sum of electronic and zero-point energies	Sum of electronic and thermal energies
		at 0 K	at 298.15 K		at 0 K	at 298.15 K
Chair TS	-231.619322407 File:Chair .LOG	-231.466705 [Script]	-231.461341 File:Chair .LOG	-234.556983 File:Chair b3lyp.LOG	-234.414919 [Script]	-234.409009 File:Chair b3lyp.LOG
Boat TS	-231.6028024 File:Boat .LOG	-231.450929 [Script]	-231.445305 File:Boat .LOG	-234.5430931 File:Boat b3lyp.LOG	-234.402340 [Script]	-234.396008 File:Boat b3lyp.LOG
Reactant (anti2)	-231.692535 File:Anti2 .LOG	-231.539539 [Script]	-231.532566 File:Anti2 .LOG	-234.611710 File:Anti2 b3lyp.LOG	-234.469203 [Script]	-234.461857 File:Anti2 b3lyp.LOG

• When the geometries for the two calculation levels are compared, significant changes in energies are reported. However, there is little change in geometries of the transition states observed.

Converted energies for different levels of theory (kcal / mol) compared to experimental data

• Energies were converted using an online converter ( for high accuracy conversion avaliable [here]. The data is reported to 3.d.p as evidence the calculations have been completed...

Theory	HF/3-21G		B3LYP/6-31G*		Experimental
Temp.	0 K	298.15 K	0 K	298.15 K
ΔE Chair TS	45.704	44.694	34.064	33.163	33.5 ± 0.5
ΔE Boat TS	55.604	54.757	41.957	41.321	44.7 ± 2.0

The data for the chair TS at the B3LYP/6-31G* level, at 298.15 K agrees very well to the literature value. The data obtained for the boat TS does not agree as favorably. This suggests that the TS calculated for the boat is less accurate than that for the chair.

It can clearly be seen that the data at the B3LYP/6-31G* level agrees much more accurately to the experimental, than that for the HF/3-21G level.

Effect of temperature on the activation energy of the reaction

• The FreqChk utility available in Guassian09W was used to obtain data at different temperatures.
• The partition function energies are reported, as there was no thermal correction to Energy avaliable in the output in command prompt - see this file which is a copy of the command prompt data: File:Freqchk315kboat.txt

The results are summarized below:

Temperature Total E (Thermal) (kcal/mol) Reactant- anti2 Boat TS Chair TS 398.15 88.085 87.189 86.456 498.15 92.158 91.106 90.485

Temperature Δ E (kcal/mol) Boat TS Chair TS 398.15 0.896 1.629 498.15 1.052 1.695

The data collected appears anomalous - the activation for the chair TS is higher than that for the boat, which is in contrast to the results obtained above.

Part 2: The Diels Alder Cycloaddition

The Diels-Alder reaction.

The Diels Alder cycloaddition has and still is the subject of a huge degree of scientific. Indeed, since the beginning of 2014 over 1,000 scientific papers have been published on the subject! Diels Alder was a revolutionary C-C bond forming reaction (to make 6-membered rings) which is of huge importance in synthetic chemistry. Although typical Diels Alder reactions require an electron rich diene and an electron rich dienophile, Inverse electron demand Diels Alder reactions are well known. The reaction is pericyclic process with a concerted cyclic transition state.

The synthetic usefulness of the Diels Alder is not limited exclusively to carbon only frameworks, but also encompasses hetero-Diels Alder reactions which allow the formation of a number hetereocylic compounds. Interestingly a rate acceleration on Diels-Alder reactions has been reported when they are carried out in water. This is of great interest to chemists, especially in the age where the reduction of hydrocarbon solvent usage is essential.

(i) Cis-butadiene The optimised cis-butadiene structure. Optimization of geometry The geometry of cis-butadiene was optimised via a semi-empirical calculation at the AM1 level. File:CISBUTADIENE OPT+FREQ AM1.LOG In a seperate calculation, the geometry of cis-butadiene was optimised sequentially at the HF/3-21G and B3LYP/6-31G* levels of theory: File:CISBUTADIENE OPT HF 3-21G.LOG File:CISBUTADIENE OPT B3LYP 6-31GD.LOG HOMO & LUMO Molecular Orbitals The HOMO and LUMO of cis-butadiene were plotted from the AM1 semi-empirical calculation, and are shown below: The HOMO orbital for cis-butadiene. The LUMO orbital for cis-butadiene. When an attempt was made to analyse the HOMO and LUMO from the higher level calculations (B3LYP/6-31G*), the MOs were much more complex. Furthermore, the HOMO was symmetric rather than the expected antisymmetric - the AM1 data was therefore used for the MOs. Q: Determine the symmetry (symmetric or anti-symmetric) with respect to the plane The HOMO is antisymmetric with respect to the plane of the molecule, whilst the LUMO is symmetric.

(ii) Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path The following structure was used as an input for the Diels-Alder (DA) transition state (TS). A distance between the ends of the 2 carbon fragment and the 4 carbon fragment of around 2.2 Å was used. A calculation at the HF/3-21G level of theory was used: Type: Opt+Freq Optimisation to: TS (Berny) Calculate Force Constants: Once Additional Keywords: Opt=NoEigen Input structure for the DA TS calculation. Output structure for the DA TS (Berny) calculation at the HF/3-21G level. The log file for the calculation is avaliable here: File:TSCALC BERNY DA HF 321G V5.LOG HOMO & LUMO Molecular Orbitals In order to determine the MOs of the system, the calculation was repeated at the semi-empirical AM1 level. The log file for the calculation is avaliable here: File:TSCALC BERNY DA AM1 321G V5.LOG a) HOMO The HOMO orbital for the DA TS. (View 1) The HOMO orbital for the DA TS. (View 2) The HOMO orbital for the DA TS. (View 3) b) LUMO The LUMO orbital for the DA TS. (View 1) The LUMO orbital for the DA TS. (View 2) The LUMO orbital for the DA TS. (View 3) Q: Determine the symmetry (symmetric or anti-symmetric) with respect to the plane The HOMO is antisymmetric with respect to the plane, whilst the LUMO is symmetric with respect to the plane. Molecular Orbitals Q: Is the HOMO at the TS s or a? The HOMO at the TS is asymmetric. Q: Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed. Whether the Diels-Alder is normal or inverse electron demand will determine whether the HOMO is located on the diene and the LUMO on the dienophile or vice versa. In this case the reaction is likely to be normal electron demand, with the HOMO located on diene (cis-butadiene) and the LUMO located on the dienophile (ethylene). The LUMO of cis-butadiene was shown to be symmetric in the previous section and the HOMO of ethylene (π bonding orbital) is also symmetric. These orbitals can therefore overlap effectively. Conversely, if the reaction were to proceed by an inverse electron demand, this is still allowed by orbital symmetry. The HOMO of cis-butadiene and the LUMO of ethylene (π* antibonding orbital) are both antisymmetric. The reaction is allowed, as both the HOMO and LUMO are of the same symmetry and therefore overlap efficiently. Geometry of the Transition State Q: What are the bond lengths of the partly formed σ C-C bonds in the TS The bond lengths of the partly formed C-C bonds in the transition state were measured as 2.20997 and 2.20899 Å. These bond lengths are very similar and are essentially equivalent when analysed at 2 d.p (2.21 Å). This provides evidence for the concerted, pericyclic nature of the Diels-Alder reaction (i.e. both bonds are formed simultaneously in a cyclic transition state). These bond lengths agree fairly well to those reported in literature for the transition state of this reaction of 2.27 ± 0.25 Å.. Q: What are typical sp3 and sp2 bond lengths? What is the Van der Waals radius of the C atom? What can you conclude about the C-C bond length of the partly formed σ C-C bonds in the TS? A typical C-C bond length for sp3 hybrididised carbon atoms in the -CH2-CH2- functionality is 1.524 Å. A typical C-C bond length for sp2 hybrididised carbon atoms in the -CH=CH- functionality is 1.478 Å. The Van der Waals radius of a carbon atom has been reported as 1.70 Å. The bond lengths obtained for the transition state appear to be significantly greater than the expected C-C radii for sp3 or sp2 hybridised C-C bonds, but within 2 x the Van der Walls radius (2 x 1.70 = 3.40 Å). This suggests there is interaction between the atoms in the transition state which is expected. Vibration that corresponds to the reaction path at the TS Imaginary Vibration (v = -817.98 cm-1) An imaginary vibration (v = -817.98 cm-1) was identified. This vibration is shown to the left of this text. There were no other immaginary vibrations. The optimised TS structure found in the LOG file appeared as below: TS for the DA reaction as appearing in LOG file. Lowest energy positive vibration (v = 166.02 cm-1) Q: Is the formation of the two bonds in the TS synchronous or asynchronous? How does this compare with the lowest positive frequency? The formation of the two bonds in the TS (corresponding to the imaginary vibration) appears to be synchronous when animated above. However, the lowest energy vibration appears to show a 'waggling' type motion between the two carbons corresponding to the ethylene reactant and the butadiene framework. In most Diels-Alder reactions, C-C bonds form very shortly (within 50 femto seconds [fs]) of the TS. The two different C-C bonds tend to form within 5 fs of each other which means that any bond stretching vibrations do not occur on a timescale which can prevent the bond forming being synchronous..

(iii) Study of the regioselectivity of the Diels Alder Reaction A calculation at the semi-empirical AM1 level of theory was used: Type: Opt+Freq Optimisation to: TS (Berny) Calculate Force Constants: Once Additional Keywords: Opt=NoEigen Exo Endo File:EXO AM1 OPTFREQ NO EIGEN V5.LOG File:ENDO TS GUESS BERNY AM1 NO EIGEN V9.LOG a) Exo TS Input structure for the DA TS calculation. Output structure for the DA TS (Berny) calculation at the AM1 level. Output structure for the DA TS (Berny) calculation at the AM1 level. An imaginary vibration (v= - 812.44 cm-1) was reported for the calculation. This vibration is animated below: The bond lengths of the forming C-C σ bonds were measured as 2.17043 Å and 2.17020 Å. Bond lengths in the TS. HOMO for Exo TS (View 1) HOMO for Exo TS (View 2) HOMO for Exo TS (View 3) b) Endo TS View 1 of the output structure for the endo TS (Berny) calculation at the AM1 level. View 2 of the output structure for the endo TS (Berny) calculation at the AM1 level. HOMO for Endo TS (View 1) HOMO for Endo TS (View 2) HOMO for Endo TS (View 3) An imaginary vibration (v= - 806.15 cm-1) was reported for the calculation. This vibration is animated below: The bond lengths of the forming C-C σ bonds were measured as 2.16241 Å and 2.16234 Å. Bond lengths in the TS. Questions Q: Give the relative energies of the exo and endo transition structures. The endo and exo TS structures were further optimised sequentially at the HF/3-21G' and then B3LYP/6-31G* levels in order to obtain representative values for the energies. The log files and energies obtained are displayed in the table below. In order to check that a TS had indeed been obtained from these re-optimisations, animated immaginary vibrations are also shown in the table for the calculations at the B3LYP/6-31G* level. The endo TS is lower in energy than the exo TS by around 2.59 kcal/mol. In this case, it is the kinetic transition state. TS Sum of electronic and thermal Energies (Hartrees) Relative Energy (kcal/mol) Log File Animated Vibration Exo -612.487661 2.589732 File:B3LYP ONCE FORCE EXO.LOG v = -448.45 cm-1 Endo -612.491788 0 File:ENDOB3LYP ONCE logfile.log v = -446.80 cm-1 Q: Comment on the structural difference between the endo and exo form. Why do you think the exo form could be more strained? TS Measurement Distance 1 / Å Distance 2 / Å Exo -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- 3.02805 3.02803 Endo -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH=CH- 2.99022 2.99022 The results in the table above, show the distances between defined atoms on the reactive fragments. The distances are around 3 Å which is within 2 x Van der Walls radius of carbon atoms (3.40 Å) which suggests there are interactions between these atoms. The entry for the exo transition state in the table above is related to steric interactions of the maleic anhydride with the -CH2-CH2- group on the other fragment. The entry for the endo transition state is related to secondary orbital interactions between the -CH=CH- and -(C=O)-O-(C=O)- fragments. As these sets of interactions occur on a distance smaller than the VdW radius, it can be seen the exo form experiences greater unfavorable steric interactions, whilst the endo form undergoes favorable secondary orbital interactions which stabilises it. Also, in both the exo and endo TS, the C-C bond distances of the forming bonds are similar - this is evidence for the concerted, pericyclic nature of the TS. The transition states for both the endo and exo forms were subjected to a NCI (Non-covalent-interactions) analysis. Areas marked green are weakly attractive, in blue strongly attractive, in yellow are weekly repulsive and in in red are strongly repulsive. TS NCI View 1 NCI View 2 Exo Endo Both transition state structures show attractive and repulsive contacts. However in the endo for, it appears that there is a greater attractive interaction between the -CH2CH2- bridge on the carbon only fragment, and the -CHCH- atoms on the other fragment than there is in the exo form. Q: Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called "secondary orbital overlap effect"? The secondary orbital overlap effect is an effect that has been envoked to explain the selectivity of the Diels Alder reaction for the endo isomer over the exo one. The theory is that there are other orbital overlap interactions that are significant in the transition state other than the HOMO - LUMO interactions. It has previously been reported that for certain reactions, these secondary orbital overlap interactions are only present in the endo TS, meaning it is formed faster and thus made preferntially. It can be seen in the endo TS above, that there is a nodal plane between the two fragments that compose the transition state. As HOMO LUMO orbital overlap is thought to be a prerequisite for getting a particular isomer, this cannot explain why the reaction proceeds. Secondary orbital overlap must therefore be envoked to explain why the endo form, the kinetic product predominates.

(iv) What effects have been neglected in these calculations of Diels Alder transition states? Some calculations have been completed at the semi-empirical AM1 force field. Semi-empirical calculations make a large number of assumptions including not completely accounting for the 2 electron Hamiltonian. The AM1 forcefield relies on the neglect of differential diatomic overlap. The calculation essentially only considers the valence electrons with the core electrons providing background charge. The calculations at the DFT (Density functional theory) level are considered to be a more accurate way of calculating energies as they reflect the experimental data better. However, they can suffer errors with intermolecular interactions..

References

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