Rep:Mod3:zsmkamwc

Module 3: Transition States and reactivity

*Note: All discussion in green was composed after 1700, 12Nov 2010

The Cope Rearrangement

The Cope rearrangement of 1,5-hexadiene was investigated and discussed in this section. The objectives of this section are to locate the low-energy minima and transition structures on the C₆H₁₀ potential energy surface by optimising and analysing the products, reactants and transitions states, in order to determine the preferred reaction mechanism.
The Cope rearrangement, which was developed by Arthur C. Cope, is an extensively studied organic reaction involving the [3,3]-sigmatropic rearrangement of 1,5-dienes. This [3,3]-sigmatropic shift rearrangement has been the subject of many experimental and computational studies. The reaction occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying slightly higher in energy.

Optimizing the Reactants and Products

Conformations of 1,5-Hexadiene

	Anti 1 Conformer BH3	Anti 3 Conformer BH3	Gauche 3 Conformer BH3
Calculation Type	FOPT	FOPT	FOPT
Calculation Method	RHF	RHF	RHF
Basis Set	3-21G	3-21G	3-21G
Charge	0	0	0
Spin	Singlet	Singlet	Singlet
C2-C5 Dihedral Angle/o	-177	180	68
Final Energy (a.u.)	-231.6926	-231.6891	-231.6927
RMS Gradient Norm (a.u.)	0.00003052	0.00003780	0.00000883
Dipole Moment (Debye)	0.2021	0.0004	0.3406
Point Group	C1	C2h	C1

Table 1: Optimisations of 1,5-Hexadiene Conformers

1,5-Hexadiene Anti 3 Conformer

The 1,5-Hexadiene with an "anti" linkage for the central four C atoms was constructed in ChemBio3D and optimised in GaussView. The carbon structures were ensured to draw anti-periplanar to each other. The optimisation was computed using the HF method with 3-21G basis set. Table 1 shows the summary of the optimisation. The optimised anti conformer is the Anti 3 conformer after comparing the structure to Appendix 1. It is because both of the conformers have the same energies and point groups. The optimisation is converged as the RMS gradient is less than 0.001. (see Table 1)

1,5-Hexadiene Gauche 3 Conformer

The Gauche form of the 1,5-Hexadiene was constructed in ChemBio3D and optimised in GaussView. The optimisation was computed using HF method with 3-21G basis set. In comparison to the Appendix 1, the optimised gauche conformer is the Gauche 3 conformer as both of them have the same point group and energy. The optimisation is converged as the RMS gradient is less than 0.001.(see Table 1)
The energy of this Gauche conformer is very similar to that of the Anti 3 conformer, however the Gauche 3 conformer is slightly lower in energy with a difference of 0.0036 a.u..(see Table 1) Thus Gauche 3 conformer is more stable then the Anti 3 conformer.

1,5-Hexadiene Anti 1 Conformer

The Anti form of the 1,5-Hexadiene was constructed in ChemBio3D and optimised in GaussView. The optimisation w
as computed using HF method with 3-21G basis set. In comparison to the Appendix 1, the optimised anti conformer is the Anti 1 conformer as both of them have the same point group and energy. The optimisation is converged as the RMS gradient is less than 0.001.(see Table 1)
According to the data in Table 1, it is clear that the Gauche 3 conformer is the most stable one with an optimised dihedral angle of 68^o. The Gauche 3 conformation has a dihedral angle close to that of idealised gauche molecule which means that there are large and unfavourable steric interactions. As the molecule is the most stable conformation, there must be a stabilising force acting on the molecule which can compensate the destabilising steric effect. This stabilising force is believed to be the hyperconjugation of the orbitals.

Method and Frequency Analysis of Anti 2 conformation

Anti 2 Conformer	HF/3-21G BH3	B3LYP/6-31G* BH3	Literature values
Calculation Type	FOPT	FOPT	/
Calculation Method	RHF	RB3LYP	/
Basis Set	3-21G	6-31G(D)	/
Charge	0	0	/
Spin	Singlet	Singlet	/
C2-C5 Dihedral Angle/o	-180	-180	/
Final Energy (a.u.)	-231.6925	-234.6117	/
RMS Gradient Norm (a.u.)	0.00002459	0.00004577	/
Dipole Moment (Debye)	0.0001	0.0005	/
Point Group	Ci	Ci	/
C=C bond length (Å)	1.316	1.333	1.340
CH2-CH bond length (Å)	1.509	1.504	1.508
CH2-CH2 bond length (Å)	1.553	1.548	1.538
CH2-CH2-CH bond angle (o)	111.4	112.7	111.5
CH2-CH=CH2 bond angle (o)	124.8	125.3	124.5

Table 2: Optimisations of 1,5-Hexadiene Anti 2 Conformer using different basis sets

1,5-Hexadiene Anti 2 Conformer

The 1,5-Hexadiene with an "anti" linkage for the central four C atoms was constructed in ChemBio3D and optimised in GaussView. The carbon structures were ensured to draw anti-periplanar to each other. The optimisation was computed using the HF method with 3-21G basis set. Table 2 shows the summary of the optimisation. The optimised anti conformer is the Anti 2 conformer after comparing the structure to Appendix 1. It is because both of the conformers have the same energies and point groups. The optimisation is converged as the RMS gradient is less than 0.001. (see Table 2)
At the very beginning, the calculations of the Anti 2 conformer had been run using the 3-21G basis set. This is a popular basis set with its fast processing time and relative accuracy when using simple atom types. Hartree-Fock (HF) is the method used with this basis set, which is a quantum mechanical method used and is used for the determination of the ground-state properties of the molecule. After the first calculations were run by HF/3-21G method, the molecule was re-optimised by the DFT method with 6-31G* basis set. This is a higher basis set then the 3-21G set which means the higher order orbitals can be more accurately defined. This allows it to have better approximations of higher row elements in calculations. The change in method and basis set has altered the calculated values of the properties of the conformer. The final energy of the conformer is slightly higher after using DFT/6-31G*method, with a difference of 2.9192 a.u.. In addition, the dihedral angle and geometry of the molecule have changed as well. From Table 2, the bond lengths from both calculations are similar to the literature values which means changing the calculation method does not affect much on the geometry of the molecule. However, the second set of the calculations are formed from a larger method and basis set. Therefore, it is assumed that the second set of results are more accurate.

Thermochemistry of the anti2 conformer

Energies	At 0 K	At 298.15 K
Sum of Electronic and Zero-point Energies (a.u.)	-233.9022	-233.9026
Sum of Electronic and Thermal Energies (a.u.)	-233.8979	-233.8983
Sum of Electronic and Thermal Enthalpies (a.u.)	-233.8970	-233.8974
Sum of Electronic and Thermal Free Energies (a.u.)	-233.930093	-233.930533

Table 3: Temperature-Dependence of Anti2-1,5-hexadiene Energies

The energy of anti2-conformer can be splitted into potential and kinetic energies. Therefore the enthalphy and free energy of dissociation can be calculated from them. The computations were repeated at two different temperatures (o K & 298.15 K) to study the effect of temperature on the energies of anti2-conformer since the parameters are temperature-dependent. (see Table 3)<br\> The results are indicated that the total energy of the molecule becomes slightly more negative as the temperature increases. This is expected as the molecule can absorb more heat at higher temperatures.

Optimizing the "Chair" and "Boat" Transition Structures

Optimisation of the Chair transition state

Properties	BH3
C-C Bond Breaking/Forming Length (Å)	2.02
Electronic Energies (a.u.)	-231.61932247
Imaginary Frequency (cm-1)	-817.92
Link	DOI:10042/to-5601

The chair TS was computed using TS(Berny) optimisation and the results are shown above. The Chair TS was also expected to calculated in another optimisation method: ModRedundant Minimisation with frozen C-C lengths (2.20 Å) which are the C atoms involved in bond breaking or forming; it then followed by a TS(Berny) Optimisation with Hessian Derivative calculation for the C-C bond breaking or forming lengths. Unfortunately, this optimisation was still failed after re-buliding the transition state and re-running the optimisation more than 4 times. The reason of the failure is still not found....The last try of the optimisation: DOI:10042/to-5643

Intrinsic Reaction Coordinate

Properties	IRC calculation with 50 points	IRC calculation with 100 points
Final Energies (a.u.)	-231.61932	-234.55698
IRC Pathway	-231.6193	-231.6151
Structure	-817.92	-764.96
Link	DOI:10042/to-5611	DOI:10042/to-5623

Table 5: Comparison of IRC Computations

The chair TS was optimised by the IRC calculation with 50 points at the first time. However, it was not converged yet. The IRC calculation was then re-computed with more atom points (100 points) to obtain a converged optimisation. Unfortunately, the reults show that the optimisation had not been converged after second IRC calculation. To improve the results, the force constant can set to be calculated in each steps instead of just once.

Optimisation of the Boat transition state

Properties	BH3
C-C Bond Breaking/Forming Length (Å)	2.14
Electronic Energies (a.u.)	-231.6028
Imaginary Frequency (cm-1)	-839.79
Vibrational image
Link

Table 6: Optimisation of Boat TS

The boat transition state was optimised using QST2 Optimisation. Table 6 shows the optimisation of the boat transition state. <br\> The imaginary frequency of boat transition state is at -839.79 cm^-1 which shows that a transition state was found. The movement of the bond at the imaginary frequency is shown in Table 6. This vibration shows asynchronous bond formation, where one bond is formed when the other one is broken (Cope Rearrangement).<br\> The calculation was failed at the first time. The boat transition state looked like the chair transition state structure but more dissociated. It was due to the linearly interpolation between the two structures (product & reactant). After relocating the boat transition state structure by changing the dihedral angle of C2-C3-C4-C5 for the reactant molecule and the inside angles of C2-C3-C4 & C3-C4-C5 for the reactant molecule, the QST2 calculation was computed successfully. <br\> The QST2 Optimisation is more time-consuming than the TS(Berny) optimisation. The exact geometry of the structures must be achieved before running the optimisation. Hence, the TS(Berny) optimisation was chosen to use instead of the QST2 optimisation in the further parts of TS optimisations.

Activation Energies

The chair and boat transition states structures were optimised using two different methods (HF/3-21G & B3LYP/6-31G*).(see Table7) Since the basis set of B3LYP/6-31G* is more accurate. the computed energies are expected to be lower than the energies computed by HF/3-21G. Since the energies are temperature dependent as explained in the previous, the calculations were then computed and compared at different temperatures (0K & 298.15K). (see Table7)

	HF/3-21G Electronic Energy (a.u.)	HF/3-21G <br\>Sum of Electronic and Zero-Point Energies (a.u.) at 0 K	HF/3-21G <br\>Sum of Electronic and Thermal Energies (a.u.) at 298.15 K	B3LYP/6-31G* Electronic Energy (a.u.)	B3LYP/6-31G*<br\>Sum of Electronic and Zero-Point Energies (a.u.) at 0 K	B3LYP/6-31G*<br\>Sum of Electronic and Thermal Energies (a.u.) at 298.15 K
Chair TS	-231.6187	-231.4655	-231.4601	-234.5572	-234.4154	-234.4092
Boat TS	-231.6030	-231.4511	-231.4455	-234.5435	234.4081	-234.4018

Table 7: Summary of energies of Chair and Boat TS

The activation energies via each transition pathway were calculated. The actiation energy for the transition state at 0K was obtained.

	HF/3-21G at 0 K	HF/3-21G <br\>at 298.15 K	B3LYP/6-31G* at 0 K	B3LYP/6-31G*<br\>at 298.15 K	Expt. <br\>at 0 K
ΔE (Chair)	47.16	44.52	34.12	33.14	33.5 ± 0.5
ΔE (Boat)	55.83	54.60	42.00	41.43	44.7 ± 2.0

Table 8: Summary of activation energies of Chair and Boat TS

Diels-Alder Cycloaddition of Cis-Butadiene and Ethene

The Diels-Alder reaction is a cycloaddition reaction between a п conjugated diene system and an alkene system to form a cyclohexene syste. It is known as a [4+2] or [п4s+п4s] cycloaddition. <br\> The reaction occurs via a concerted transition state in which two sigma bonds are formed between the terminated atoms of the two conjugated п system.<br\> The Diels-Alder Cycloaddition of cis-butadiene and ethene was shown on the left.<br\><br\><br\>

Optimisation of Reactants

Optimisation of Cis-Butadiene

Energy of Cis-Butadiene

Properties
Electronic Energy (a.u.)	-155.98648966
Sum of Electronic and Zero-Point Energies (a.u.)	-155.901143
Sum of Electronic and Thermal Energies (a.u.)	-155.896439
Sum of Electronic and Thermal Enthalpies (a.u.)	-155.895494
Sum of Electronic and Thermal Free Energies (a.u.)	-155.927848
Structure	BH3

Table 9: Energy of Cis-Butadiene

The optimisation of Cis-butadiene was computed using DFT/B3LYP/6-31G* method. The summary of the energies is shown in Table 9

Molecular Orbitals of Cis-Butadiene

HOMO

LUMO

The HOMO, LUMO of cis butadiene are shown on the both sides. The HOMO (highest occupied molecular orbital) of cis-butadiene is anti-symmetric (AS) with respect to the reflection plane of the molecule, since the phases are inverted. <br\> On the other hand, the LUMO (lowest occupied molecular orbital) is symmetric (S) with respect to the reflection plane of the molecule, as the molecule can reflect in the plane of symmetry.<br\> The assignments of orbital symmetry are important in pericyclic reaction since they determine whether the reaction will occur or not and the stereochemistry of the product.<br\><br\><br\><br\>

Optimisation of Ethene

Energy of Cis-Butadiene

Properties
Electronic Energy (a.u.)	-78.58745830
Sum of Electronic and Zero-Point Energies (a.u.)	-78.536229
Sum of Electronic and Thermal Energies (a.u.)	-78.533187
Sum of Electronic and Thermal Enthalpies (a.u.)	-78.532243
Sum of Electronic and Thermal Free Energies (a.u.)	-78.557104
Structure	BH3

Table 10: Energy of Ethene

The optimisation of Ethene was computed using DFT/B3LYP/6-31G* method. The summary of the energies is shown in Table 10

Molecular Orbitals of Ethene

HOMO

LUMO

The HOMO, LUMO of ethene are shown on the both sides. The HOMO (highest occupied molecular orbital) of ethene is symmetric (S) with respect to the plane of symmetry since the molecule can reflect in the plane of symmetry. <br\> On the other hand, the LUMO (lowest occupied molecular orbital) is anti-symmetric (AS) with respect to the reflection plane of the molecule, as the phases are inverted.<br\> The symmetries of the HOMO and LUMO in ethene are opposite to the HOMO and LUMO in cis-butadiene. According to the conservation of orbital symmetry which states that only orbitals of the same symmetry can interact, the Diels-Alder Cycloaddition of cis-butadiene and ethene can be occured. It is owing to the interactions between the HOMO of cis-butadiene and the LUMO of ethene, also between the LUMO of cis-butadiene and the HOMO of ethene.<br\><br\><br\>

Optimisation of Transition State

The optimisation and Frequency calculation to a TS(Berny) using DFT/B3LYP/6-31G* method with additional keyword: Opt=NoEigen of the transition state was conducted in this section. <br\> The TS(Berny) optimisation was chosen to use rather than QST2 optimisation due to the strict requirements in the QST2 optimisation.

Energy of Transition State

Properties
Electronic Energy (a.u.)	-234.54389646
Sum of Electronic and Zero-Point Energies (a.u.)	-234.403323
Sum of Electronic and Thermal Energies (a.u.)	-234.396906
Sum of Electronic and Thermal Enthalpies (a.u.)	-234.395962
Sum of Electronic and Thermal Free Energies (a.u.)	-234.432889
Imaginary Frequency (cm-1)	-524.74
C-C Bond Forming Length (Å)	2.27
Structure	BH3
Link	DOI:10042/to-5618

Table 11: Energy of Transition State

The summary of the energies is shown in Table 11.Since different calculation method presents energies in different way, it is no point to compare the energies between two different methods. However, better geometry of a molecule in an optimisation can be obtained using different calculation method. DFT/B3LYP/6-31G* was chosen to use as it is more accurate than the HF/3-21G method.

MOs of Transition State

HOMO

LUMO

The HOMO and LUMO of the transition state are shown on both sides.<br\> From the comparison of the Molecular Orbitals of the transition state and of the reactants, it is seen that the HOMO of the transition state was derived from the overlap of the HOMO in cis-butadiene and the LUMO in ethene. Furthermore the LUMO in transition state is built up by the LUMO in cis-butadiene and the HOMO in ethene. This can again be explained by the conservation of orbital symmetry which has been introduced previously. It also fits with the MO theory as only filled orbitals can overlap with empty orbitals.<br\> To compare the energies of the molecular orbitals of the reactants, it is obvious that the overlap of the HOMO in cis-butadiene and the LUMO in ethene will form an orbital in lower energy than the overlap of the LUMO in cis-butadiene and the HOMO in ethene.

From Transition State to Product

Vibrational Frequencies

Imaginary Freq

Lowest positive Freq

<br\><br\>The Imaginary vibration of the TS indicate bond breaking or forming interactions in the transition state, which can either lead forward to the products or backward to the reactants. The forzen animation of the imaginary vibration of the transition state is shown on the left. From the frozen animation, it is observed that the formation of the two bonds is synchronous as expected in the concerted Diels-Alder reaction. The lowest positive frequency vibrates at 135.93 cm^-1 which is shown on the right. The transition state in this case is asynchronous in contrast to the imaginary vibration. On end of the cis-butadiene and ethene terminated atom move towards each other, where at the other end they move away from each other. <br\><br\><br\><br\><br\><br\><br\>

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

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

<br\>The reaction between cyclohexa-1,3-diene and maleic anhydride is a Diels-Alder reaction as well. However, this reaction is slightly defferent from the previous one. Two products are formed in this reaction as shown on the left. <br\> The endo and exo products are diastereomers and their fomations depend on which direction will the diene (cyclohexa-1,3-diene) attack on the dienophile (maleic anhydride). In most cases, endo isomer is the major product of the Diels-Alder reaction. And for this reaction, the endo isomer is the major product. <br\><br\><br\>

Optimisation of Reactants

Optimisation of Cyclo-1,3-hexadiene

Energy of Cyclo-1,3-hexadiene

Properties
Electronic Energy (a.u.)	-233.4189
Sum of Electronic and Zero-Point Energies (a.u.)	-233.2961
Sum of Electronic and Thermal Energies (a.u.)	-233.2909
Sum of Electronic and Thermal Enthalpies (a.u.)	-233.2900
Sum of Electronic and Thermal Free Energies (a.u.)	-233.3244
Structure	BH3
Link	DOI:10042/to-5607

Table 12: Energy of Cyclo-1,3-hexadiene

The optimisation of Cyclo-1,3-hexadiene was computed using DFT/B3LYP/6-31G* method. The summary of the energies is shown in Table 12.

MOs of Cyclo-1,3-hexadiene

HOMO

LUMO

<br\><br\>The HOMO and LUMO of cyclo-1,3-hexadiene are shown on both sides. The HOMO of cyclo-1,3-hexadiene is anti-symmetric (AS) with respect to the reflection plane of the molecule. The LUMO of cyclo-1,3-hexadiene is symmetric (S) since it is symmetrical after the reflection with respect to the symmetry plane. This results are similar to the results in cis-butadiene. <br\><br\><br\><br\><br\><br\>

Optimisation of Maleic Anhydride

Energy of Maleic Anhydride

Properties
Electronic Energy (a.u.)	-380.52307388
Sum of Electronic and Zero-Point Energies (a.u.)	-380.443727
Sum of Electronic and Thermal Energies (a.u.)	-380.437852
Sum of Electronic and Thermal Enthalpies (a.u.)	-380.436908
Sum of Electronic and Thermal Free Energies (a.u.)	-380.474570
Structure	BH3
Link	DOI:10042/to-5609

Table 13: Energy of Maleic Anhydride

The optimisation of Maleic Anhydride was computed using DFT/B3LYP/6-31G* method. The summary of the energies is shown in Table 13.

MOs of Maleic Anhydride

HOMO

LUMO

<br\><br\><br\>The HOMO and LUMO of Maleic Anhydride are shown on both sides. Both of the HOMO and LUMO of maleic anhydride are anti-symmetric (AS) with respect to their plane of symmetry since the phases of both molecules are inverted.<br\> The calculation shows the energy of the LUMO is negative, but it is actually expected to be positive.<br\><br\><br\><br\><br\>

Optimisation of Transition State

The optimisation and Frequency calculation to a TS(Berny) using DFT/B3LYP/6-31G* method with additional keyword: Opt=NoEigen of the transition state was conducted in this section.

Energy of Transition State

Properties	Endo TS	Exo TS
Electronic Energy (a.u.)	-613.81228374	-613.79219413
Sum of Electronic and Zero-Point Energies (a.u.)	-613.614062	-613.593962
Sum of Electronic and Thermal Energies (a.u.)	-613.602080	-613.581548
Sum of Electronic and Thermal Enthalpies (a.u.)	-613.601135	-613.580604
Sum of Electronic and Thermal Free Energies (a.u.)	-613.652616	-613.634018
Imaginary Frequency (cm-1)	-523.73	-1335.75
C-C Bond Forming Length (Å)	1.60	2.11
Structure	BH3	BH3
Link	DOI:10042/to-5621	DOI:10042/to-5622

Table 14: Energies of Endo and Exo Transition States

The imaginary freqencies of both isomers show that the optimised structures are transition states. The RMS gradients of both isomers are less than 0.001 which means both isomers are optimised. However it seems like the optimisations were not successfully obtained. (see the TS structures in Table 14) This can be improved by increasing the C-C bond forming lengths before running the optimisations. <br\> Nevertheless the obtained results are still reliable although they are not the best one. The energies of both isomers are still reasonable. (see Table 14) The endo transition state is lower in energy which can then be concluded that it is more stable than the exo transition state. The difference in energies of the endo and exo transition states can be attributed to secondary orbital interactions in the endo transition state, which can then stabilise the structure.
Furthermore the endo transition state is expected to have lower activation energy than the exo transition state. Thus the endo transition state is predicted to give a kinetic product of the reaction. <br\><br\> As the optimisations of both isomers are not completed and there is lack of time to re-run the optimisations and frequencies calculations again, the molecular orbitals of transition states and the vibrational frequencies sections are failed to discuss.

Stereoselectivity in Diels-Alder Reactions

The selection of the endo product in this reaction follows the Alder's endo rule which leads to a lower energy transition state and hence reacts more rapidly. This selectivity can also be explained by secondary orbital interactions and Woodward-Hoffmann rules for pericyclic reactions. <br\> The primary orbital overlap in both transition states is the bonding interaction between the terminated atoms of the conjugated pi system in the HOMO of cyclo-1,3-hexadiene and the pi* C=C of the LUMO of maleic anhydride. This leads to the formation of two sigma bonds between the terminated atoms of the two pi systems. Nonetheless there is another favourable bonding interaction in the endo transition state. This is between the pi* C=O of the LUMO of maleic anhydride and the centre carbons of the conjugated pi system in the HOMO of cyclo-1,3-hexadiene, hence it stabilises the endo transition state. <br\> For the endo product, there is secondary orbital bonding interaction between the centre carbon of the pi conjugated system in the cyclo-1,3-hexadiene and the carbon atom of the pi* C=O orbital. The shared electron density between these orbitals passes from the top face of the pi conjugated system to the back of the molecule, which passes through the bottom face of the maleic anhydride to the orbital on the carbon atom of the pi* C=O orbital. This overlap stabilises the endo product and therefore it is lower in activation energy. <br\> On the contrary, there is no such orbitals overlap is observed in the exo transition state. Thus the endo transition state is lower in energy than the exo transition state, hence the endo product is expected to be the kinetic product. A kinetic product usually dominates in an irreversible reaction, so the endo product dominates the reaction as the Diels-Alder reaction is irreversible.<br\>