Rep:Mod:ia2514 TS

(This is a very heavy page. You should move the Jmols to another page as it currently takes a few minutes to load Tam10 (talk) 15:50, 7 February 2017 (UTC))

Introduction

Studying reactions of complex molecules, identifying transition states and the optimised structures of reactants and products requires numerically solving the Schrödinger equation, a task which cannot be completed manually. Fortunately, computational chemistry offers various means of investigating chemical structures and reactions, one of which is the Density Functional Theory (DFT). The basis of DFT methods lies in the assumption that the energy of a system can be determined from the electron density function. However, DFT methods can be computationally demanding. A faster, but less accurate alternative is given by semi-empirical methods, which are based on the Hartree-Fock method (a method to calculate the wave function by approximating it), but employ empirically determined parameters.

By starting from a given structure, these computational methods can probe the potential energy surface locally in order to find a minimum energy geometry or a transition structure. Reactants and products appear as local minima on the potential energy surface, where the gradient (first derivative) is zero and the curvature (second derivative) is positive in all directions. Transition states represent saddle points, where the gradient is again zero (they are stationary points), but the curvature is negative in one direction and positive in all others. One way to distinguish between these two different types of stationary points is therefore the number of negative frequencies resulted from a frequency calculation: a minimum has no negative frequencies, whereas a transition state presents one negative frequency (corresponding to the reaction path). Once the transition state is located, an intrinsic reaction coordinate (IRC) calculation can be run in order to determine the path of minimum energy between reactants and products passing through that transition state.

In this experiment, the transition states for the cycloaddition reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, xylylene and sulfur dioxide were located using the semi-empirical PM6 method. This allowed for further investigation of the reactions, including reoptimising using the DFT B3LYP method, visualising the interacting molecular orbitals, determining the kinetic and thermodynamic products and observing bond making and breaking processes.

Nf710 (talk) 10:37, 8 February 2017 (UTC) Nice intro TS correctly defined, and good brief knowledge of the methods

Exercise 1

Figure 1. Diels-Alder reaction between butadiene and ethylene

Figure 2. MO diagram for the butadiene + ethylene reaction

For the investigation of the Diels-Alder reaction between butadiene and ethylene (figure 1), the transition state was located using method 2: both ethylene and butadiene were optimised to a minimum, the resulting structures were arranged together to resemble the transition state, the distances between the reacting carbon termini were set to 2.20 and 2.24 Å, respectively and then frozen, followed by an optimisation to a minimum. The resulting structure was optimised as a transition state which presented one negative frequency vibration corresponding to the reaction and an IRC was run on the resulting geometry, allowing for the extraction of the product structure which was further optimised to a minimum. All calculations were performed using the semi-empirical PM6 method and the frequency calculations of neither the reactants, nor the products presented any negative frequencies.

The reaction between butadiene and ethylene can be understood in terms of frontier molecular orbitals. The MO diagram in figure 2 illustrates the interactions between the butadiene end ethylene HOMO and LUMO and the 4 resulting transition state molecular orbitals. The shape of the frontier orbitals of the reactants as obtained from the PM6 frequency calculations (figures 3-6) is in accordance with the shapes drawn in figure 2. As expected with an increase in the number of conjugated π bonds, the HOMO-LUMO energy gap decreases for butadiene with respect to ethylene, the orbital order being consistent with the energy calculation performed for the reactants.

Figure 3. Ethylene HOMO	Figure 4. Ethylene LUMO

Figure 5. Butadiene HOMO	Figure 6. Butadiene LUMO

For two orbitals to interact, they need to have the same symmetry, which indicates that in order for a reaction to proceed, the interacting frontier orbitals need to be both either symmetric or asymmetric. In both of these cases, the orbital overlap integral is non-zero. If no such interaction is possible, the reaction is 'forbidden' (and the orbital overlap integral for a symmetric-asymmetric interaction is zero). In the case of the butadiene and ethylene Diels-Alder reaction the frontier orbitals interacting are the HOMO of the dienophile with the LUMO of the diene (both symmetric) and the LUMO of the dienophile with the HOMO of the diene (both asymmetric). These two pairs of interactions each lead to the formation of a bonding and an anti-bonding molecular orbital, giving a total of four transition state molecular orbitals. Due to the similar energy gaps between the interacting pairs of reactant orbitals, it is difficult to predict which interaction leads to the formation of the HOMO of the transition state. The order of the transition state molecular orbitals can nonetheless be inferred from the frequency calculation, suggesting that the interaction between the symmetric frontier orbitals is the one that leads to the formation of the transition state HOMO and LUMO. The orbitals resulting from the frequency calculation (figures 7-10) can be correlated to the corresponding molecular orbitals in the diagram (figure 2) as indicated by the labels.

Figure 7. TS MO #16	Figure 8. TS MO #17	Figure 9. TS MO #18	Figure 10. TS MO #19

The change in bond lengths as the reaction proceeds is plotted in figure 11 and some of the key values are presented in table 1. As expected for a concerted reaction, the lengths of C1-C4 & C6-C7 and C7-C11 & C14-C1, respectively, remain the same throughout the reaction. The length of the initial three double bonds (C1-C4, C6-C7, C11-C14) increases as they all become single bonds in the product (C11-C14 is finally slightly longer than C1-C4 and C6-C7 since it is a bond between two sp³ hybridised carbons, rather than one sp³ and one sp² like in the latter case). The length of the C4-C6 single bond in the butadiene decreases during the course of the reaction, becoming a double bond. The C7-C11 and C14-C1 lengths decrease as the reactants approach each other, forming single bonds in the product. Overall, C=C double bonds have typical lengths of 1.33-1.34 Å, C-C single bonds between two sp³ hybridised carbons are 1.54 Å long, whereas C-C single bonds between one sp³ and one sp² carbon are 1.50 Å long. The length of the bonds between the reacting carbon termini in the transition state (C7-C11, C14-C1) is smaller than twice the Van der Waals radius of carbon (1.70 Å), suggesting that there is a level of bonding between each of the two pairs of carbon atoms (weaker than a single bond).

Figure 11. Adjacent C-C bond lengths throughout the reaction

Table 1. C-C bond lengths (Å) at different stages in the reaction

	Reactants (infinite separation)	Transition state	Product
C1-C4&C6-C7	1.34	1.38	1.50
C7-C11&C14-C1	$\mathrm{\infty }$	2.11	1.54
C4-C6	1.47	1.41	1.34
C11-C14	1.33	1.38	1.54

As expected, the optimised structure of the transition state presented one negative frequency corresponding to the reaction path. The vibration, illustrated in figure 12, shows that the Diels-Alder reaction between butadiene and ethylene is a concerted process in which the formation of the two new C-C bonds is synchronous.

Figure 12. TS negative frequency vibration

Nf710 (talk) 10:57, 8 February 2017 (UTC) Nice first section well written, you havent shown any understanding of the electron demand of the reaction in terms of orbitals. But everything elese was good.

Exercise 2

Figure 13. Diels-Alder reaction between cyclohexadiene and 1,3-dioxole

Figure 14. MO diagram for the cyclohexadiene + 1,3-dioxole reaction

In order to study the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole, the transition state was located using method 2. Both reactants were optimised to a minimum and the resulting structures were positioned in the approximate geometry of the transition state with the bonds between the reacting carbon termini frozen at a length of around 2.20 Å. The obtained geometry was optimised to a minimum, followed by an optimisation to a transition state. This structure was used to run an IRC calculation and the resulting product was optimised to a minimum. The calculations for both the endo and the exo adduct were performed at the PM6 level, followed by optimisations of the reactants (cyclohexadiene, 1,3-dioxole), transition states (endo, exo) and products (endo, exo) using the DFT B3LYP method and the 6-31G(d) basis set. The frequency calculations for the reactants and products presented no negative frequencies, whereas in the case of each of the transition states one negative frequency corresponding to the reaction path could be observed.

As shown in figures 15-22, the transition state molecular orbitals for both the endo and the exo adduct follow the same order as in the case of the butadiene + ethylene reaction. The HOMO and the LUMO of the transition state are both symmetric, indicating that they were formed as a result of the interaction between the HOMO of the dienophile and the LUMO of the diene. This suggests that the Diels-Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse electron demand reaction, in which the dienophile is electron rich and/or the diene electron poor. This is, as expected, in accordance with the structure of 1,3-dioxole: the two oxygens bonded to the sp² carbons donate electron density into the double bond, raising the energy of the HOMO and the LUMO of the dienophile. Furthermore, the order of the reactant orbitals is also confirmed by the energy calculation performed for cyclohexadiene and 1,3-dioxole as extracted from the IRC calculations. These observations allowed for the necessary adjustments in the energy levels of the orbitals in figure 14.

(Very neat diagrams, but why are there disconnections in the MO diagram? Tam10 (talk) 15:50, 7 February 2017 (UTC))

Figure 15. ENDO TS MO #40	Figure 16. ENDO TS MO #41	Figure 17. ENDO TS MO #42	Figure 18. ENDO TS MO #43

Figure 19. EXO TS MO #40	Figure 20. EXO TS MO #41	Figure 21. EXO TS MO #42	Figure 22. EXO TS MO #43

Figure 23. Steric clash in the endo and exo products

The values of the Gibbs free energies at room temperature of the reactants, transition states and products as recorded from the outputs of the calculations, along with the calculated activation energies and reaction Gibbs free energies are presented in table 2. The formation of the endo product has both the lower activation energy and the more negative (higher in absolute value) reaction Gibbs free energy, implying that it is both the kinetically and thermodynamically favoured product. This result can be explained by considering the structures of the two transition states and products. In the endo transition state, the oxygen p orbitals can interact with the middle diene carbons through a secondary orbital interaction which is not possible in the case of the endo adduct. It can thus be observed in figure 16 that the endo transition state HOMO involves stabilising, in-phase interactions between the oxygen p orbitals and the diene middle carbons p orbitals, which therefore lead to a decrease in the energy of the transition state and an increase in the rate of the reaction following this path. Similar interactions are not observed in the case of the exo transition state (figure 20), deeming it the less kinetically favoured path. The thermodynamic preference for the endo product arises from its stability with respect to the exo adduct. As shown in figure 23, the exo product suffers from steric clash due to the angle of the hydrogen atoms (bonded to sp³ carbons), whereas the endo product does not exhibit any steric clash (hydrogen atoms bonded to sp² carbons).

Table 2. Cyclobutadiene + 1,3-dioxole Diels-Alder reaction energies

	Cyclohexadiene Gibbs free energy		1,3-dioxole Gibbs free energy		Reactants Gibbs free energy (infinite separation)		Transition state Gibbs free energy		Product Gibbs free energy		Activation energy	Reaction energy
	Hartrees	kJ/mol	Hartrees	kJ/mol	Hartrees	kJ/mol	Hartrees	kJ/mol	Hartrees	kJ/mol	kJ/mol	kJ/mol
endo	-233.3	-612591.4	-267.1	-701187.4	-500.4	-1313778.8	-500.3	-1313622.1	-500.4	-1313849.3	156.75	-70.46
exo							-500.3	-1313614.2	-500.4	-1313845.7	164.59	-66.87

Nf710 (talk) 11:22, 8 February 2017 (UTC) Excellent section, you have got the correct energies and your understanding of the thermo and kinetic products is excellent. your drawing of the steric clashes is excellent.

Exercise 3

Figure 24. Xylylene + SO₂ reaction scheme

As seen in figure 24, xylylene and SO₂ can react both through a Diels-Alder reaction and through a cheletropic process. For the investigation of the Diels-Alder reaction, the transition state was firstly located using method 3. The structure of the product was optimised to a minimum, ensuring that no negative frequencies could be observed. The xylylene and SO₂ fragments were separated in the resulting structure at 2.0 Å for the C-O bond and 2.4 Å for the C-S bond. The obtained geometry was firstly optimised to a minimum, followed by an optimisation to a transition state, an IRC calculation and an optimisation of the product. The use of this method led to the formation of the exo transition state and product, so for the investigation of the endo transition state method 2 was used. The reactants (xylylene and SO₂) were optimised to a minimum, arranged together to resemble the transition state, the reacting termini bonds were frozen and the resulting geometry optimised to a minimum, followed by an optimisation to a transition state. Finally, an IRC calculation was run and the endo product optimised. The cheletropic reaction was followed by employing method 3 as well (as described above), by separating the fragments at C-S distances of 2.3 Å and 2.4 Å, leading to an optimisation of the transition state and product. All calculations were performed using the semi-empirical PM6 method.

Figure 25. Endo IRC

Figure 26. Exo IRC

Figure 27. Cheletropic IRC

Figures 25-27 present animations of the progress of the three reactions. It can be observed that during the course of the reaction, the single bonds in the 6 membered ring become shorter, whereas the initially double bonds lengthen, resulting in the formation of an aromatic ring with C-C bond lengths in-between single and double carbon-carbon bonds. Indeed, this is confirmed by the actual values of the bond lengths: initially, the single bonds are 1.47-1.49 Å long and the double bonds 1.35 Å, values which increase during the reaction until they reach 1.39-1.42 Å in the aromatic product. The IRCs also reveal that the Diels-Alder reactions are asynchronous (the C-O bonds form before the C-S bonds), whereas the cheletropic reactions are synchronous (both C-S bonds form at the same time).

Table 3. Xylylene + SO₂ reaction energies

	Xylylene Gibbs free energy	SO2 Gibbs free energy	Reactants Gibbs free energy (infinite separation)	Transition state Gibbs free energy	Product Gibbs free energy	Activation energy		Reaction energy
	Hartrees	Hartrees	Hartrees	Hartrees	Hartrees	Hartrees	kJ/mol	Hartrees	kJ/mol
endo Diels-Alder	0.178528	-0.119266	0.059262	0.090559	0.021704	0.031297	82.17	-0.037558	-98.61
exo Diels-Alder				0.092077	0.021455	0.032815	86.16	-0.037807	-99.26
cheletropic				0.099059	-0.000002	0.039797	104.49	-0.059264	-155.60

Figure 28. Xylylene + SO₂ reaction profile

(Don't use curved lines for these as it implies this is the curvature for the RC. Straight lines joining the energy levels are fine Tam10 (talk) 15:50, 7 February 2017 (UTC))

The Gibbs free energies of the reactants, transition states and products for the three reactions along with the calculated activation energies ΔG^‡ and reaction energies Δ_rG are summarised in table 3. The obtained values allowed for the construction of the reaction profile in figure 28 indicating that the endo Diels-Alder adduct is the kinetic product (lowest activation energy) and that the cheletropic reaction leads to the most thermodynamically favoured product (most negative reaction energy). The fact that the fastest reaction path proceeds via the endo transition state is in accordance with the presence of secondary orbital interactions between the p orbital of the non-reacting oxygen and the p orbitals of the diene middle carbons (as explained previously). This interaction is not possible in the exo geometry (or the cheletropic transition state).

Figure 29. Alternative Xylylene + SO₂ Diels-Alder reaction scheme

The alternative Diels-Alder reaction possible between SO₂ and the xylylene diene inside the ring (figure 29) was studied using method 2 at the PM6 level for both paths (endo transition state and product, exo transition state and product). The corresponding energy values are summarised in table 4 and by comparison with the energies for the other three reactions possible (table 3), they suggest that this alternative Diels-Alder path is both kinetically (higher ΔG^‡) and thermodynamically disfavoured (positive Δ_rG). It is expected that this alternative path is slower than the previously presented reactions since access to the out-of-ring diene is easier than to the ring diene. The thermodynamic stability of the products from the previous three reactions with respect to the alternative Diels-Alder is consistent with the fact that they are aromatic compounds, whereas the products obtained from reactions at the ring diene are not. The absence of aromatisation as a driving force therefore makes the products in figure 29 less thermodynamically favoured.

Table 4. Xylylene + SO₂ alternative Diels-Alder reaction energies

	Xylylene Gibbs free energy	SO2 Gibbs free energy	Reactants Gibbs free energy (infinite separation)	Transition state Gibbs free energy	Product Gibbs free energy	Activation energy		Reaction energy
	Hartrees	Hartrees	Hartrees	Hartrees	Hartrees	Hartrees	kJ/mol	Hartrees	kJ/mol
endo	0.178528	-0.119266	0.059262	0.10207	0.06561	0.042808	112.39	0.006348	16.67
exo				0.105055	0.067304	0.045793	120.23	0.008042	21.11

Conclusion

Computational chemistry calculations (using both semi-empirical and DFT methods) performed for three different pairs of reactants undergoing cycloadditions allowed for the investigation of the reactions. The orbital symmetry requirements for the Diels-Alder reaction were discussed in the case of the butadiene + ethylene and the molecular orbitals obtained from frequency calculations were correlated with those in the MO diagram. The reaction between cyclohexadiene and 1,3-dioxole proved to be an inverse demand reaction in which the endo product is both the kinetic and thermodynamic product. Finally, the various ways in which xylylene and sulfur dioxide can react were studied in terms of energy barriers and reaction energies, indicating that the endo Diels-Alder adduct formed by reaction at the out-of-ring diene is the kinetic product, whereas the cheletropic reaction is the thermodynamically favoured path.