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Problems in Structural Inorganic Chemistry$

Wai-Kee Li, Yu-San Cheung, Kendrew Kin Wah Mak, and Thomas Chung Wai Mak

Print publication date: 2012

Print ISBN-13: 9780199658497

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199658497.001.0001

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(p.299) Appendix 7 Electrocyclic Reactions and Cycloadditions

(p.299) Appendix 7 Electrocyclic Reactions and Cycloadditions

Source:
Problems in Structural Inorganic Chemistry
Publisher:
Oxford University Press

The molecular orbitals of butadiene can be used to predict, or at least rationalize, the course of reactions this compound undergoes. For instance, experimentally it is known that


                     Appendix 7
                   Electrocyclic Reactions and Cycloadditions

In 1965, American chemists R. B. Woodward and R. Hoffmann (“conservation of orbital symmetry”– Woodward–Hoffmann Rules) and Japanese chemist K. Fukui (“frontier orbital theory”) proposed theories to explain these results as well as those for other related reactions. Woodward won the Nobel Prize in Chemistry in 1965 for his synthetic work. In 1981, after the death of Woodward, Hoffmann and Fukui shared the same prize for the theories discussed here.

These theories assert that the course of an electrocyclic reaction that a compound undergoes is controlled by its “highest occupied molecular orbital (HOMO)”. Referring to reactions A7.1 and A7.2, we pictorially illustrate the four π MOs of butadiene in Fig. A7.1.

For a thermal reaction ofbutadiene [reaction (A7.1)] (“ground state chemistry”), the HOMO is ψ 2 (reaction pathways shown in Fig. A7.2). For a photochemical reaction of butadiene [reaction (A.7.2)] (“excited state chemistry”), the HOMO is ψ 3 (reaction pathways shown in Fig. A7.3).

(p.300)


                     Appendix 7
                   Electrocyclic Reactions and Cycloadditions

Fig. A7.1 The four π molecular orbitals of butadiene.


                     Appendix 7
                   Electrocyclic Reactions and Cycloadditions

Fig. A7.2 The thermal electrocyclic reaction of butadiene.

(p.301)

                     Appendix 7
                   Electrocyclic Reactions and Cycloadditions

Fig. A7.3 The photochemical electrocyclic reaction of butadiene.

For wavefunction ψ 2, the terminal atomic orbitals ϕ 1 and ϕ 4 have the relative orientations shown in Fig. A7.1. It is now clear from Fig. A7.2 that a conrotatory process leads to a bonding interaction between ϕ 1 and ϕ 4, while a disrotatory process leads to an antibonding interaction between ϕ 1 and ϕ 4. In other words, the conrotatory pathway is allowed, while the disrotatory one is forbidden.

Conversely, for wavefunction ψ 3, the terminal atomic orbitals ϕ 1 and ϕ 4 have the relative orientations also shown in Fig. A7.1. Now, as illustrated in Fig. A7.3, a conrotatorypathwayyields an antibonding interaction between the terminal atomic orbitals, while a disrotatory step leads to a stabilizing bonding interaction. Hence now the disrotatory process wins out.

Now let us apply this theory to the electrocyclic reaction of hexatriene:


                     Appendix 7
                   Electrocyclic Reactions and Cycloadditions

The wavefunctions of the six π molecular orbitals of hexatriene are summarized in the following table:

(p.302)

Energies

Wavefunctions

E 6 = α − 1.802β

ψ 6 = 0.232ϕ 1

−0.418ϕ 2

+0.521ϕ 3

−0.521ϕ 4

+0.418ϕ 5

−0.232ϕ 6

E 5 = α − 1.247β

ψ 5 = 0.418ϕ 1

−0.521ϕ 2

+0.232ϕ 3

+0.232ϕ 4

−0.521ϕ 5

+0.418ϕ 6

E 4 = α − 0.445β

ψ 4 = 0.521ϕ 1

−0.232ϕ 2

−0.418ϕ 3

+0.418ϕ 4

+0.232ϕ 5

−0.521ϕ 6

E 3 = α + 0.445β

ψ 3 = 0.521ϕ 1

+0.232ϕ 2

−0.418ϕ 3

−0.418ϕ 4

+0.232ϕ 5

+0.521ϕ 6

E 2 = α + 1.247β

ψ 2 = 0.418ϕ 1

+0.521ϕ 2

+0.232ϕ 3

−0.232ϕ 4

−0.521ϕ 5

−0.418ϕ 6

E 1 = α + 1.802β

ψ 1 = 0.232ϕ 1

+0.418ϕ 2

+0.521ϕ 3

+0.521ϕ 4

+0.418ϕ 5

+0.232ϕ 6


                     Appendix 7
                   Electrocyclic Reactions and Cycloadditions

Fig. A7.4 The thermal and photochemical electrocyclic reactions of hexatriene.

For the thermal and photochemical electrocyclic reactions of hexatriene, the controlling HOMOs are ψ 3 and ψ 4, respectively. As Fig. A7.4 shows, the allowed pathway for the thermal reaction is disrotatory. On the other hand, the allowed pathway for the photochemical reaction (p.303) is conrotatory. These results are just the opposite we found for the electrocyclic reactions of butadiene (Figs. A7.2 and A7.3).

To summarize, for a linear polyene with 4, 8, 12,… π electrons involving in its thermal electrocyclic reaction, the reaction will follow a conrotatory pathway; conversely, its photochemical electrocyclic reaction will adopt a disrotatory pathway. On the other hand, for a linear polyene electrocyclic reaction with 6, 10, 14,… π electrons involved, the pathways of its thermal and photochemical electrocyclic reactions will be disrotatory and conrotatory, respectively.

The best known cycloaddition may well be the Diels–Alder reaction between butadiene and ethylene (under thermal conditions):


                     Appendix 7
                   Electrocyclic Reactions and Cycloadditions

According to the frontier orbital theory, the orbitals that control these reactions are the aforementioned HOMO of one reactant and the LUMO (lowest unoccupied molecular orbital) of the other reactant. So, for this reaction, we have two possible scenarios: interaction between HOMOψ 2 of butadiene and LUMO ϕ of ethylene or that between HOMO π of ethylene and LUMO ψ 3 of butadiene. As the following illustration indicates, both possibilities lead to bonding overlap between the interacting orbitals of the reactants; so the reaction is allowed, as we all know. In addition, as found by theory, between these two possible scenarios, we favor the interaction between the HOMO of the electron-rich reactant (butadiene in this case) with the LUMO of the electron-poor reactant (ethylene).


                     Appendix 7
                   Electrocyclic Reactions and Cycloadditions (p.304)

On the other hand, the dimerization of ethylene is symmetry-forbidden, as illustrated below:


                     Appendix 7
                   Electrocyclic Reactions and Cycloadditions

In order for this [2 + 2] cycloaddition (each of the reactants has two π electrons participating in the interaction) to proceed, we need to carry out the experiment under photochemical conditions, where both the HOMO of the excited ethylene [with configuration (π)1(π )1] and the LUMO of the ground-state ethylene [configuration (π)2(π )0] are π . As the following illustration reveals, now we have a symmetry-allowed situation:


                     Appendix 7
                   Electrocyclic Reactions and Cycloadditions

To summarize, the [2 + 2] cycloadditions will proceed photochemically, but not thermally. On the other hand, the [2 + 4] cycloadditions such as Diels–Alder reactions are allowed thermally and forbidden photochemically.

REFERENCE: I. Fleming, Molecular Orbitals and Organic Chemical Reactions: Student Edition, Wiley, Chichester, 2009, pp. 215–6; pp. 304–7.