Rep:MOD:xj1213TS

Abstract

In this experiment, the transition states of the Cope rearrangement and two Diels-Alder cycloaddition reactions were modelled and calculated using Gaussian 09W and Gaussview 5.0 via different optimisation methods. The structures of the transition states and the activation energies were then investigated to support the preferred pathways of the reactions.

Nf710 (talk) 11:20, 22 April 2016 (BST) You could have spoken bout the methods here

The Cope Rearrangement Tutorial

The Cope Rearrangement is a [3+3]-sigmatropic rearrangement, which is one of the pericyclic reaction involving the intramolecular shift of a σ bond. The reaction is concerted and both 'Chair' and 'boat' conformations are possible in the transition state.

File:XjCope rearrangement.png

Scheme 1. The Cope Rearrangement Reaction Mechanism and Transition States

Optimizing the Reactants and Products

In the following sections, different conformations of 1,5-hexadiene were studied. The possibility of various different conformers of 1,5-hexadiene is due to the free rotation around the central C-C bond of the molecule.

Optimization of 1,5-hexadiene Conformers

A number of conformers of 1,5-hexadiene were prepared with GaussView and were optimised using the HF/3-21G level of theory. Results are shown in Table 1. There are two main groups of conformers: anti and gauche. For the anti conformers, the dihedral angle of the four central carbon atoms (C₂-C₃-C₄-C₅) is 180^o, whereas that of the gauche conformers is 60^o. The dihedral angles of C₁-C₂-C₃-C₄ and C₃-C₄-C₅-C₆ determine the specific anti or gauche conformers.

The first two calculated low energy conformers are anti 1 and gauche 4. The calculated energy shows that the anti-structure is more stable than the gauche structure. The phenomenon can be explained by steric hindrance of the gauche structure. As shown on Figure 1a, the anti-periplanar conformer is more sterically favoured because the two alkene groups are as far apart as possible minimising the steric clash, whereas the two alkene groups are close to each other in the gauche conformation, increasing the energy.

Nf710 (talk) 11:54, 22 April 2016 (BST) Nice use of newman projects to explain steric

File:Xj1213ciecleprojectionantigauche.png

Figure 1. a) Anti-periplanar conformer b) Gauche conformer of butadiene

However, the anti 1 is not the most stable conformer of 1,5-hexadiene. Repeating the optimisation of a slightly twisted gauche structure gives a more stable gauche 3 stureture. The deviation from the above statement suggests that the overall stabilisation of a conformer is not purely determined by steric factor. This can be rationalised by looking into the HOMO of the structures of all the conformers which had been optimised. The stability of the gauche 3 conformer is due to the in-phase overlapping π_C-C orbitals between the two terminal double bonds as well as the presence of CH/π hydrogen bonds. This interactions have great contribution to the stability of the gauche 3 structure. Only weak π_C-C-σ_C-H interaction between each of the alkenes and the neighbouring C-H bond is observed in the case of anti 1 conformer. In the case of the gauche 4 conformer, there is no stereoelectronic interaction. Hence, it has the highest energy of all.

Table 1. Optimised conformations with energy, point group and HOMO

Conformer	Structure	HF/3-21GEnergy / hartrees	Point Group	HOMO
Anti1	15hexadiene anti stru	-231.69260	$C_2$	File:15hexadiene anti stru HOMO.png
Gauche4	15hexadiene gauche stru	-231.69153	$C_2$	File:15hexadiene gauche stru HOMO.png
Gauche3	15hexadiene gauche3 stru	-261.69266	$C_1$	File:15hexadiene gauche3 stru HOMO.png

Nf710 (talk) 11:13, 25 April 2016 (BST) Good use of MOs to explain the ordering

Comparison of Different Levels of Theory

In order to calculate the energy of the transition state of 1,5-hexandiene, the anti 2 conformer was optimised using HF/3-21G followed by the B3LYP/6-31G(d) level of theory. As different basis sets and methods were used, the energies of the two different levels of theory cannot be compared. Hence comparisons can only be made regarding to the change of geometry. Comparisons of the calculated predictions and experimentally measured bond lengths (Table 3) and dihedral angles (Table 4) clearly show that the DFT methods are more accurate. The molecule calculated using HF/3-21G gives both shorter bond lengths and smaller dihedral angles. In addition, the H-C-H angle of the central carbon changed to a smaller angle (Table 5). All of these give evidence of change in geometry. However, the very small variation in the geometry between these two levels of theory suggested the effectiveness and accuracy of the HF/3-21G level of theory in rapid analysis of small molecular systems.

Table 2. Summary for Anti 2 conformer at different levels of theory

Level of Theory	Structure	Energy / hartrees	Point Group	HOMO
HF/3-21G	15hexadiene anti2 stru	-231.69254	$C_i$	15hexadiene anti2 stru HOMO
B3LYP/6-31G(d)	15hexadiene anti2DTF stru	-231.61171	$C_i$	File:15hexadiene anti2DTF stru HOMO.png

Table 3. Summary of Bond Length for Anti 2 conformer at different levels of theory

Bond Lengths
Atoms	HF/3-21G / Å	B3LYP/6-31G(d) / Å	Experimental / Å
C1-C2	1.33352	1.31615	1.340 ± 0.003
C2-C3	1.50426	1.50888	1.508 ± 0.012
C3-C4	1.54806	1.55282	1.538 ± 0.027

Table 4. Summary of Dihedral Angle for Anti 2 conformer at different levels of theory

Dihedral Angle
Atoms	B3LYP/6-31G(d) / °	HF/3-21G / °	Experimental / °
C1-C2-C3-C4	118.627	114.698	120
C2-C3-C4-C5	179.985	179.995	168

Table 5. Summary of H-C-H angle for Anti 2 conformer at different levels of theory

H-C-H
HF/3-21G / °	B3LYP/6-31G(d) / °
107.7	106.7

Nf710 (talk) 11:59, 25 April 2016 (BST) You can compare relative energy changes. but well understood, the hamiltonians are totally different

Thermochemitry

A frequency calculation was then carried out based on the previously constructed B3LYP/6-31G(d) anti 2 conformer in order to confirm the structure is at its energy minimum. All the vibrational modes are associated with positive frequencies indicating that the optimisations were successful giving a structure with local minimum energy.

From the output log file, energy readings can be obtained under Thermochemistry section. Four different energies at 298 K and 0K are listed below (Table 6). Firstly, as shown in the table, the sum of electronic and zero-point energies are equal at both temperatures as expected. This value is the potential energy of the molecule at 0 K and only electronic and zero-point energy are included. Secondly, the sum of electronic and thermal energies indicates the total energy of the molecule in standard conditions. This adds up translational, vibrational, rotational and electronic motions, which gives a higher energy value than that at 0 K. The next row gives the total energy with an additional contribution from RT. Finally, the sum of electronic and thermal free energies takes into account of the entropic contribution to the total energy of the molecule. Furthermore, at 0K, the only sources of energy is the ground state electronic energy and the zero-point residue vibrational energy. Therefore the values in all rows of 0 K are the same.

Table 6. Thermochemistry Information for anti 2 conformer in B3LYP/6-31G(d) theory at 0 K and 298 K

Entry	Energy	Calculation at 0 K / Hartrees	Calculation at 298 K / Hartrees
1	Sum of electronic and zero-point Energies	-234.469214	-234.469214
2	Sum of electronic and thermal Energies	-234.469214	-234.461866
3	Sum of electronic and thermal Enthalpies	234.469214	-234.460922
4	Sum of electronic and thermal Free Energies	-234.469214	-234.500798

Nf710 (talk) 12:26, 25 April 2016 (BST) Good understanding of the contributions to the energy

Optimizing the "Chair" and "Boat" Transition Structures

As stated above, one of the possible transition state is ‘chair’ conformation, which was optimised using a ‘guess’ structure. The structure was constructed with two HF/3-21G pre-optimised allylic fragments, which is energetically similar to the transition state. The distance between each pair of the terminal carbon which corresponded to bond breaking and forming was set to 2.2 Å.

Optimization of Chair TS with Guess Method

Two different methods were used to optimise the ‘chair’ TS. The first one was direct optimisation + frequency calculation with ‘’’QA(berny)’’’ method. The force constant was calculated once with additional keyword ‘’’Opt=NoEigen’’’. The purpose of the keyword was to prevent the generation of multiple imaginary frequencies. A single imaginary frequency of was found, confirming the transition state.

Table 7. Summary for allyl at HF/3-21G level of theory

Allyl Fragment Structure	HF/3-21G Energy / hartrees	Point Group
File:Allyl hf321G stru.png	-115.82304	$C_{2v}$

Table 8. Summary for chair TS at HF/3-21G level of theory

Chair TS Structure	HF/3-21G Energy / hartrees	Imaginary Frequency (-817.82 cm-1)
Allyl TS	-231.61932

Optimization of Chair TS with the Frozen Method

Another method to optimise the chair TS is by freezing the terminal carbon which corresponded to bond breaking and forming to 2.2 Å. The minimum energy configuration of the allyl fragments can be found at HF/£-21G level of theory. An additional keywords Opt=ModRedundant was included in the optimisation. After freezing the bonds, the structure was re-optimised to a transition state as the Gauss method. The previously frozen bonds were set as a 'derivative'.

Chair TS Structure	HF/6-21G Energy / hartrees	Imaginary Frequency (-817.99 cm-1)
Chair ts guess freez stru	-231.61932

Comparison of Guess and Frozen Coordinates Method

The point group of the chair TS is C_2h. By comparing both the energies and the imaginary frequencies calculated from the two different methods, it is obvious that they are very similar with only negligible difference. This indicates that the guess structure is very close to the real structure of the transition state, therefore both methods gives very close results which are of high accuracy.

The vibration given by the imaginary frequency provided the expected transformation from the reactant to the product back and forth. The animation above shows that while one sigma bond is forming the other sigma bond breaks. This is consistent with the reaction scheme 1 shown at the beginning of the report. The shortening of the bonds also indicates the formation of the double bonds.

Optimization to Boat TS Using QST2

The ‘boat’ transition state was optimised using the QST2 method at the HF/3-21G level of theory. This method does not need a ‘guess’ structure. Instead, by modelling the structures of the reactants and products and interpolation of these two input structures, the structure of the transition state can be found. At first, twp pre-optimised ‘’anti2’’ structure with Ci symmetry was put in separate windows as the unmodified reactant and product. After careful labelling of the atoms, the optimisation and frequency calculation was performed at HF/3-21G level of theory with the ‘’’Ts(QST2)’’’ method. The failure of the calculation suggests that the QST2 method requires the structure of the reactant and product to resemble the transition state. The calculation was then set up with specified structure and geometry to match the ‘boat’ transition state, which successfully proceeded.

File:Boatboatlabelling.PNG

Figure 2. Labelling of the Reactant and Product

Boat TS Structure	HF/6-21G Energy / hartrees	Imaginary Frequency (-839.96 cm-1)
Boat qst2ahh stru	-231.61170611

Intrinsic Reaction Coordinate of Chair TS

Further analysis of the reaction process can be done by looking at the the Intrinsic Reaction Coordinate (IRC) after the frozen coordinate method at the HF/3-21G level of theory. The Total Energy along IRC (Figure 2) and RMS Gradient Norm along IRC (Figure 3) are plotted respectively. The IRC calculates the forward and backward reaction paths from the TS structure. Meanwhile, it also provides geometries of the structures along the reaction coordinate defined by the number of points, N. The force constants were set to be calculated every time it reached the next step.

As the reactant and product are essentially the same, the IRC calculation only considered the forward direction with N=50. The reaction terminated at N=44 with an energy of -231.692 Hartrees, which corresponds to the region where the RMS gradient norm approaches zero. This shows that the energy no longer changes. Further optimisation at this point was carried out at the HF/3-21G level of theory to obtain the lowest energy structure. The final structure appears to be the ‘’gauche 2’’ conformer.

File:Total energy along IRC.PNG

Figure 2. Total energy along IRC

File:RMS gradient norm along IRC.PNG

Figure 3. RMS gradient norm along IRC

IRC optimised Structure	HF/3-21G Energy / hartrees
Chair IRC first 44	-231.692

Optimization of Chair and Boat TS with B2LYP/6-31G(d)

The 'chair' and 'boat' transition state structures were reoptimised at a higher level of theory, B3LYP/6-31G(d). The results are summarised below.

Boat Transition Structure	Imaginary Frequency (-530.36cm-1)	B3LYP/6-31G(d) Energy / Hartrees
Boat ts 631Gd stru		-234.543093

Chair Transition Structure	Imaginary Frequency (-565.23cm-1)	B3LYP/6-31G(d) Energy / Hartrees
Chair ts 631Gd stru		-234.556983

Activation Energies

The tables shown below summarise the major thermochemical data obtained from the frequency calculations for the ‘’chair TS’’, ‘’boat TS’’ and ‘’anti2’’ conformer (reactant) using HF/3-21G and B3LYP/6-31G(d) levels of theory respectively. The activation energy can be calculated by the energy difference between the chair/boat TS and the reactant. The calculations at B3LYP/6-31G(d) level of theory have closer values to the experimental results as expected. Moreover, It is clearly shown that the chair transition state is favoured over the boat transition state by providing a lower energy pathway. The reason behind this is likely to be the repulsion of the hydrogen at the axial position. Additionally both activation barriers decrease with increasing temperature.

Table xx. Summary of energies (in hartree)

	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	-231.619322	-231.466697	-231.461337	-234.556983	-234.414930	-234.409009
Boat TS	-231.611706	-231.450928	-231.445299	-234.543093	-234.402342	-234.396008
Reactant (anti2)	-231.692535	-231.539540	-231.532566	-234.611710	-234.469203	-234.461856

*1 hartree = 627.509 kcal/mol

Table xx Summary of activation energies (in kcal/mol)

	HF/3-21G	HF/3-21G	B3LYP/6-31G*	B3LYP/6-31G*	Expt.
	at 0 K	at 298.15 K	at 0 K	at 298.15 K	at 0 K
ΔE (Chair)	45.71	44.70	34.06	33.16	33.5 ± 0.5
ΔE (Boat)	55.60	54.76	41.96	41.32	44.7 ± 2.0

The Diels-Alder Cycloaddition

The Diels-Alder reaction is a [4+2] cycloaddition which is also one kind of pericyclic reactions. This reaction involves a converted formation of two σ bonds from two different conjugated π systems. The notation [4+2] refers to the number of π electrons involved from the two systems. In this case, a diene and a dienophile react to give a six-membered cycloaddition product. The diene is required to adopt an s-cis conformation in order to allow the reaction to take place.

Diels Alder Cycloaddition of cis-butadiene and ethylene

File:Xj1213DA1.png

Scheme 2. Diels Alder reaction mechanism for cis-butadiene and ethene

Optimization of cis-butadiene and ethylene

The structures of cis-butadiene and ethene were optimised using semi-empirical/AM1 method followed by a B3LYP/6-31G(d) optimisation for comparison. In addition, the structure of trans-butadiene was also optimised for comparison. The results are summarised below. A further frequency calculation shows that there was one imaginary frequency for the cis-butadiene showing that the cis-structure was not the most stable conformation of butadiene. There were no negative frequencies for the trans-butadiene and ethylene confirming that they were at their minimum energies. The energy of the trans-butadiene is slightly lower than that of the cis-butadiene further confirming that the trans-butadiene is a more favourable.

(Well spotted. There is also a minimum for cis-butadiene where the dihedral angle between the carbons is about 10º, further complicating the reaction path Tam10 (talk) 11:01, 14 April 2016 (BST))

The calculated HOMO of cis-butadiene and LUMO of ethene are both antisymmetric whereas the LUMO of cis-butadiene and HOMO of ethene are both symmetric. These MO’s confirm that the cycloaddition reaction happens due to the overlap of the HOMO and LUMO.

Molecule	Structure	Semi-Empirical/AM1 Energy / Hartrees	B3LYP/6-31G(d) Energy / Hartrees	Point Group	HOMO	LUMO
Cis-butadiene	Cisbutadiene opt stru	0.04879719	-155.985951	C2v	Cisbutadiene HOMO2	Cisbutadiene LUMO
Trans-butadiene	File:Transbutadiene opt stru.png	0.04756288	-155.992145	C2h	Transbutadiene HOMO	Transbutadiene LUMO
Ethylene]	Ethylene opt stru	0.02619028	-78.587459	D2h	Ethylene opt HOMO	Ethylene opt LUMO

Molecule	Imaginary Frequency (Semi-Empirical/AM1) / cm-1	Imaginary Frequency (B3LYP/6-31G*) / cm-1	Imaginary Vibration	First Real Frequency (Semi-Empirical/AM1) / cm-1	First Real Frequency (B3LYP/6-31G*) / cm-1	First Real Vibration
Cis-butadiene	-39.44	-125.32		312.44	295.34
Trans-butadiene	-	-	-	87.52	177.22
Ethylene	-	-	-	834.54	835025

Optimization of cis-butadiene and ethylene TS

The transition state of this reaction was optimised using the TS(Berny) at the Semi-Empirical/AM1 level of theory followed by a calculation at the B3LYP/6-31G(d) level of theory for comparison. Only one imaginary frequency was found for each method confirming the presence of the transition state. The animation of the vibration illustrates the formation of the two sigma bonds with the decrease in the through space bond distance and the formation of a new double bond between C₂-C₃ by showing the bond stretches and compressions.

The HOMO and LUMO of the product were analysed in order to study the interactions between the reactants. The Woodward Hoffman rules were applied to evaluate the MOs of the transition state structure. Using the frontier molecular orbital (FMO) theory and the visualised MO from Gaussview, it was noted that the symmetries of the reactants and transition state must be consistent for a reaction to be classed allowed. Hence, it was clearly shown that the symmetric LUMO of butadiene and symmetric HOMO of ethene form the symmetric LUMO of the transition state. Likewise, the antisymmetric HOMO of butadiene and the antisymmetric LUMO of ethene form the antisymmetric HOMO of the transition state.

The vibrational movement of the imaginary frequency of the transition state can be described as synchronous as it has symmetric movement; the fragments ends mutually come towards each other resembling the formation of the bonds. On the other hand, the lowest positive frequency is asynchronous as the vibrational movement is not symmetric and the fragments ends do not come close together.

Structure	Semi-Empirical/AM1 Energy / Hartrees	B3LYP/6-31G(d) Energy / Hartrees	HOMO (antisymmetric)	LUMO (symmetric)
File:DA1 ts opt am1 stru.png	0.111655	-234.543896	File:DA1 ts opt am1 HOMO.png	File:DA1 ts opt am1 LUMO.png

Levels of Theory	Imaginary Frequency / cm-1	Vibration (synchronous)	First Real Frequency / cm-1	Vibration (asynchronous)
Semi-Empirical/AM1	-956.09		147.32
B3LYP/6-31G(d)	-525.34		135.92

The bond lengths of the transition states that were calculated from the two different levels of theory were compared and summarised below. The bond lengths were only recorded to 3 s.f..

File:DA1 label.png

The C₁-C₂, C₂-C₃ and C₅-C₆ are all shorter than the typical C-C single bond but longer than the C=C double bond. This indicates the resonance of electron density across all the C-C bond in the transition state. The through space bond length between the terminal carbons (C₄-C₅ and C₁-C₆) are longer than C-C single bond but smaller than the total of two Van der Waals radii (3.4 Å) suggesting the formation of C-C bond across the two reactant.

	C1-C2/ Å	C2-C3/ Å	C5-C6/ Å	C1-C6/ Å	Lit C=C bond/ Å	Lit C-C bond/ Å	C Van Der Waals Radius / Å
AM1 Semi Empirical	1.38	1.40	1.38	2.12	1.334	1.544	1.70
B3LYP/6-31G*	1.38	1.41	1.39	2.27

Diels Alder Cycloaddition of Cyclohexa-1,3-diene and Maleic Anhydride

File:DA2endoexodfujxfgjhhhhhhh.png

Scheme 3. Diels Alder reaction mechanism between maleic anhydride and buta-1,3-diene

Optimization of Maleic Anhydride and Cyclohexa-1,3-diene

The regioselectivity of the Diels Alder reaction was investigated through the reaction between Maleic anhydride and cyclohexa-1,3-diene. Maleic anhydride is an electron poor dienophile due to the presence of two electron withdrawing carbonyl groups, therefore lowers the energy of the dienophile. Thus the hypothesis of this reaction would be that the LOMO of maleic anhydride will interact with teh HOMO of the cyclohexa-1,3-diene for a better interaction. The two cycloaddition products will be produced, endo and exo. The activation energies were calculated for each approach.

Molecule	Structure	Semi-Empirical/AM1 Energy / Hartrees	Point Group	HOMO	LUMO
Maleic Anhydride	Cisbutadiene opt stru	0.04879719	C2v	Cisbutadiene HOMO2	Cisbutadiene LUMO
Cyclohexa-1,3-diene	File:Cyclohexa13diene opt stru.png	0.04756288	C2	Cisbutadiene HOMO2	Cisbutadiene HOMO2

Optimization of Endo-TS and Exo-TS

As summarised below, the energies and imaginary frequencies of the endo and exo transition states are very similar. However, the endo transition state is slightly lower in energy, indicating that the endo-product is more favourable.

(This indicates that it is kinetically favourable Tam10 (talk) 11:01, 14 April 2016 (BST))

TS	Structure	Semi-Empirical/AM1 Energy / Hartrees	HOMO	LUMO
Endo-TS	File:Endo da am1 stru.png	-0.051505	File:Endo da am1 HOMO.png	File:Endo da am1 LUMO.png
Exo-TS	File:Exo da opt am1 stru.png	-0.050420	File:Exo da opt am1 HOMO.png	File:Exo da opt am1 LUMO.png

TS Structure	Imaginary Frequency / cm-1	Vibration	First Real Frequency	Vibration
Endo-	-808.43		62.44
Exo-TS	-812.16		60.82

The bond lengths of the transition states were measured and compared with the literature C-C bond lengths. The C₁-C₂, C₁-C₆ and C₇-C₁₀ bond lengths are in between the bond lengths of C-C single and double bonds as expected, which indicates the breaking and forming of the double bonds. The distances between C₅-C₇ and C₂-C₁₀ which are longer than a C-C single bond but shorter than the sum of two carbon Van der Waals radius indicate the potential formation of the sigma bonds as expected. The vibrational motions from the imaginary frequencies also showed the movements of the reactants during the formation of the products via the transition state. The imaginary frequencies confirmed the successful modelling of the transition states.

TS	Structure	C1-C2/ Å	C2-C3/ Å	C3-C4/ Å	C1-C6/ Å	C7-C8/ Å	C5-C7/ Å	C7-C10/ Å	Lit C=C bond/ Å	Lit C-C bond/ Å	C Van Der Waals Radius / Å
Endo-TS	DA2 labeling endo	1.39	1.49	1.52	1.40	1.49	2.16	1.41	1.334	1.544	1.70
Exo-TS	File:DA2 labeling exo.png	1.39	1.49	1.52	1.40	1.49	2.17	1.41

Activation Energy

Thermochemistry data was extracted from the frequency analysis and activation energies were calculated.

As shown in the tables, the endo transition structure has lower energy meaning that the activation barrier is lower, hence the reaction would preferably proceed via the endo path. Further comparison can be achieved by further calculation at another level of theory (e.g. B3LYP/6-31G(d)) and the accuracy and efficiency of the two methods can be compared.

	Electronic energy	Sum of electronic and zero-point energies	Sum of electronic and thermal energies
		at 0 K	at 298.15 K
Endo TS	-0.051505	0.133494	0.143683
Exo TS	-0.050420	0.133494	0.143683
maleic anhydride	0.048797	-0.063346	-0.058192
1,3-cyclohexadiene	0.047562	0.152502	0.157726

	at 0 K	at 298.15 K
ΔE (Endo) / kcal mol-1	36.59	36.44
ΔE (Exo) / kcal mol-1	37.46	37.20

(No mention of secondary orbital overlap or sterics Tam10 (talk) 11:01, 14 April 2016 (BST))

Conclusion

In conclusion the computational experiment has successfully simulated two of the pericyclic reactions by calculations of the cyclic transition state structures using QST2 or TS(Berny) methods. Three different levels of theories were used: HF/3-21G, B3LYP/6-31G(d) and simi-empirical/AM1. One of the advantages of computational simulation is that it simulates an IR spectrum for the transition state of an reaction which would be impossible experimentally. However more complex calculations with the methods used in this experiment may not be accurate as solvent effects has been ignored.