Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole
Figure 1: Reaction scheme of Diels-Alder reaction of cyclohexadiene and 1,3-dioxole.
The Diels-Alder (D-A) reaction of cyclohexadiene and 1,3-dioxole can proceed in 2 pathways, exo and endo pathways. In exo pathway, the oxygens in 1,3-dioxole is oriented away from the diene component of cyclohexadiene in transition state whereas in endo pathway the oxygens in 1,3-dioxole is oriented towards the diene component of cyclohexadiene in transition state.
Method Used In Optimization and Analysis
Method 3 was employed in locating the transition state by which the product was drawn and optimized to minimum at PM6 level. With the optimized product, the C-C single bonds formed during the reaction of cyclohexadiene and 1,3-dioxole were deleted, froze at 2.20 Å and optimized to minimum at PM6 level to identify the frozen guess transition state. The distance 2.20 Å is the approximate separation between the reacting termini in guess transition state. It is a value between a C-C single bond length and their combined Van der Waals radii. The guess TS structure was then optimized at PM6 level and the PM6 optimized TS was used to run a IRC calculation. The reactants, exo and endo products obtained from first and last frame of IRC calculation were optimized to minimum at PM6 level. All the PM6 optimized reactants, TS and products were then reoptimized with a more accurate calculation, B3LYP/6-31G(d).
Optimized Reactants, Transition Structure and Products at B3LYP/6-31G(d) Level
Table 1: Optimized Reactants at B3LYP/6-31G(d) Level.
Cyclohexadiene
1,3-Dioxole
Table 2: Optimized Transition State and Product of Endo and Exo Pathways at B3LYP/6-31G(d) Level.
Reaction Pathway
Transition State
Product
Exo Pathway
Endo pathway
The geometry of reactants, transition state and product are checked to properly converge with their respective stationary points are found in log files. In addition, transition state has only one imaginary frequency and it is then visualized to ensure a correct transition state structure is obtained. There is no imaginary frequency obtained in reactants and products.
MO Analysis
MO Diagram of Exo and Endo Pathway
(Fv611 (talk) Your Mo diagrams are very nice. Could have expended a bit more on the differences between endo and exo conformations in term of their relative MO energies.)
Table 3: MO Diagram for The Formation of Cyclohexadiene/1,3-Dioxole TS.
Exo Pathway
Endo Pathway
Figure 1: MO diagram for the formation of the exo TS with basic symmetry labels shown; A= Antisymmetric and S= Symmetric.
Figure 2: MO diagram for the formation of the endo TS with basic symmetry labels shown; A= Antisymmetric and S= Symmetric.
MO of Reactants, Product and Transition Structure
Table 4: Frontier MO of Cyclohexadiene, 1,3-Dioxole and Exo and Endo TS.
Reactants
Transition State
Orbital Interaction and Discussion
Cyclohexadiene
1,3-Dioxole
Exo
Endo
LUMO, MO23, S
HOMO, MO19, S
HOMO, MO41, S
HOMO, MO41, S
“+” stands for an in-phase combination and “-” stands for an out-of-phase interaction
“+” stands for an in-phase combination and “-” stands for an out-of-phase interaction
Cyclohexadiene (HOMO, MO22, A) + 1,3-dioxole (LUMO, MO20, A) = TS (HOMO-1, MO40, A)
Cyclohexadiene (HOMO, MO22, A) - 1,3-dioxole (LUMO, MO20, A) = TS (LUMO+1, MO43, A)
LUMO+1, MO43, A
LUMO+1, MO43, A
Normal or Inverse Demand DA Reaction
A single point energy calculation reveals the relative energy levels of HOMO and LUMO of the reactants, cyclohexadiene and 1,3-dioxole. An IRC calculation was first performed and the first frame which contains both reactants was used to carry out a single point calculation of both endo and exo pathway. The Table 5 below shows the HOMO and LUMO obtained from a single point energy calculation of the exo pathway. The HOMO and LUMO from a single point energy calculation for endo pathway is not shown as the shape of MOs are the same as the exo pathway but their relative energies and energy gap are tabulated in Table 6 and 7.
Table 5: MO of Reactants from Single Point Energy Calculation of Exo Pathway.
Reactant
Molecular Orbital
HOMO
LUMO
Cyclohexadiene
MO29, A
MO31, S
1,3-Dioxole
MO30, S
MO32, A
Table 6: Relative Energy Levels of Reactants obtained from Single Point Energy Calculation For Exo and Endo Pathways.
Reactant
Orbital Energy/ a.u.
Exo Pathway
Endo Pathway
HOMO
LUMO
HOMO
LUMO
Cyclohexadiene
-0.32217
+0.02111
-0.32135
+0.02288
1,3-Dioxole
-0.32207
+0.02979
-0.31696
+0.03219
Table 7: Energy Gap of Normal and Inverse Electron Demand D-A Reaction.
Reaction Type
Orbital Combination
Energy Gap/ a.u.
Exo Pathway
Endo pathway
Normal Electron Demand
HOMO (Cyclohexadiene) + LUMO (1,3-Dioxole)
0.352
0.354
Inverse Electron Demand
HOMO (1,3-Dioxole) + LUMO (1,3-Cyclohexadiene)
0.343
0.340
The reactivity or the outcome of pericyclic reaction is controlled by the relative energies of the Frontier Molecular Orbitals (FMOs) which are the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital). Frontier molecular orbital theory states that a reaction is only allowed if there is favourable mixing (constructive and in-phase combination) between HOMO and LUMO of the reactants [1]. This results in 2 types of Diels-Alder (D-A) reaction. The normal electron demand Diels-Alder reaction occurs between the electron deficient dienophile (low energy LUMO) and the electron rich diene (high energy HOMO) [2]. In contrast, the species involved in an inverse electron demand D-A reaction is the electron rich dienophile (high energy HOMO) and the electron deficient diene (low energy LUMO) [2]. Both combinations are symmetry allowed and result in a small energy difference between the FMOs, hence enhancing their orbitals interaction.
By referring to the MO diagram in Table 3, the HOMO of cyclohexadiene is of the same symmetry as the LUMO of 1,3-dioxole and the vice versa. Both interactions are thus allowed because of the matching in phases. However, based on the single point energy calculation in Table 6, the HOMO and LUMO of 1,3-dioxole is higher in energy than that of cyclohexadiene. This is due to the electron donating ability of oxygen lone pair of electron into the π system in 1,3-dioxole, raising its HOMO and LUMO energy. Hence, the calculated energy gap in Table 7 between the 1,3-dioxole HOMO and the cyclohexadiene LUMO (inverse electron demand D-A) is smaller than that between cyclohexadiene HOMO and 1,3-dixole LUMO and (normal electron demand D-A). Since a smaller energy gap giving rise to a stronger HOMO-LUMO interaction, hence the D-A reaction between the 1,3-dioxole and cyclohexadiene is an inverse electron demand D-A reaction.
Nf710 (talk) 22:38, 21 February 2018 (UTC) This is an excellent section well done. Excellent single point energy analysis of the reactant FMOS
Thermochemistry
Table 8: Thermochemistry Data at B3LYP/6-31G(d) Level.
Species
Sum of Electronic and Thermal Free Energies/ 105 kJmol-1
Cyclohexadiene
-6.1259319
1,3-Dioxole
-7.0118878
Sum of Reactant Energy
-13.1378197
Exo TS
-13.1361433
Endo TS
-13.1362216
Exo Product
-13.1384578
Endo Product
-13.1384938
Table 9: Reaction Barriers and Reaction Energies
Reaction Pathway
Reaction Barriers/ 105 kJmol-1
Reaction Energies/ 105 kJmol-1
Exo Pathway
+167.64
-63.81
Endo Pathway
+159.81
-67.41
Activation energy is the minimum kinetic energy that reactant(s) must acquire to overcome the energy barrier to have a productive chemical reaction. It is the Gibbs free energy difference between the total of reactant’s energies and transition structure. The lower the activation energy of a reaction, the higher the rate of reaction and hence it is more kinetically favourable and vice versa. The reaction energy determined exclusively by the Gibbs free energy difference between reactants and product and is completely independent of the reaction pathway as Gibbs free energy is a state function.
ΔG = ΔH − TΔS, where ΔG is the Gibbs free energy, ΔH is the enthalpy change, T is the Kelvin temperature and ΔS is the entropy change.
An exothermic reaction, with an enthalpy change < 0, the Gibbs free energy change will also be < 0 (a spontaneous process) unless entropy change is large and negative. An endothermic reaction, with an enthalpy change > 0, the Gibbs free energy change will also be > 0 (a non-spontaneous process) unless entropy change is large and positive. Hence, the product of a more exothermic reaction is thermodynamically more stable (lower in energy) and always favoured.
In the D-A reaction between a cyclohexadiene and 1,3-dioxole, the endo pathway has a lower reaction barrier and is more exothermic than the exo pathway. The endo TS and product both have lower (more negative) Gibbs free energy and thus are more stable than the respective exo TS and product. Hence, it is concluded that the kinetically and thermodynamically favoured product is endo product based on B3LPY/6-31G(d) calculation. This is quite different from the most famous D-A reaction of cyclopentadiene and maleic anhydride in which the exo product is thermodynamic product and the endo product is kinetic product.
Nf710 (talk) 22:39, 21 February 2018 (UTC) Your energies are correct and your analysis has included an exclennt discussion on thermodynamics.
Table 10: Orbital Interaction in Transition Structures and Products and Sterics in Products of Exo and Endo Pathway.
Reaction Pathway
Orbital Interaction
Sterics Interaction in Product
Discussion
Transition Structure
Product
Exo
HOMO, MO41, S
HOMO, MO41, S
The HOMOs in TS and product for both pathways is the combination of 1,3-dioxole HOMO and cyclohexadiene LUMO. In exo pathway, there is no secondary orbital interaction observed in HOMO of TS and product as the oxygen is orientated away from the diene component. Contrastingly, a significant secondary orbital interaction is observed between the lone pair in non-bonding p orbital of oxygen and diene component of cyclohexadiene. This in-phase interaction across the space between the orbitals although no real bonds are formed is favourable and stabilizes the endo TS to a lower energy, leading to decrease in the activation barrier and hence it is favoured under kinetic control D-A reaction. This stabilizing secondary orbital interaction is also observed in the endo product and lowering its energy. Hence, the endo pathway is more exothermic and is favoured under thermodynamic control D-A reaction.
As shown in diagram, there is small amount of steric clash between H6, H8 and H23 of tetrahedral sp3 carbon atoms in exo product and destabilizes the exo product slightly. The corresponding steric clash is less in endo product because H5 and H6 bonded to a trigonal planar sp2 (Note: The endo product is oriented in this way to compare with the exo product). Hence, the exo product is less stable and higher in energy than endo product, which is against the outcome of the most famous D-A reaction between cyclopentadiene and maleic anhydride.
Endo
HOMO, MO41, S
HOMO, MO41, S
Simplified Diagram of Primary and Secondary Orbital Interaction
Table 11: Primary and Secondary Orbital Interaction in Exo and Endo Pathway.
Reaction Pathway
Exo
Endo
Orbital Interaction
Nf710 (talk) 22:41, 21 February 2018 (UTC) These diagrams are excllent and your discussion is again really good. There is not much room for improvement in the section well done.
↑E. V. Anslyn, D. A. Dougherty, Modern Physical Organic Chemistry, University Science Books, Sausalito, United States, 2006.
↑ 2.02.1K.N. Houk, Acc. Chem. Res., 1975, 8(11), 361-369, DOI:10.1021/ar50095a001 . Cite error: Invalid <ref> tag; name ":1" defined multiple times with different content
↑ J. Clayden, N. Greeves, S. Warren, P. Wothers, Organic Chemistry, Oxford University Press Inc., New York, 2001.
