A Conceptually Simple Approach to the Analysis of Aromaticity in

Research: Science & Education

A Conceptually Simple Approach to the Analysis of Aromaticity in Pericyclic Transition States Richard Francis Langler Department of Chemistry, Mount Allison University, Sackville, New Brunswick, Canada E0A 3C0

Three major approaches have been developed to predict outcomes for concerted reactions controlled by orbital symmetry: (i) correlation diagrams (1), (ii) frontier orbital interactions in transition states (2), and (iii) incipient aromatic/antiaromatic character in transition states (3–5). The latter (Zimmerman-Dewar) approach (3–5) recognizes two distinct types of reacting systems: (i) those involving 4N+2 electrons and (ii) those involving 4N electrons in monocyclic p-orbital arrays. In Figure 1, the disrotatory transition state is said to be “cyclobutadiene-like” and therefore “antiaromatic”. The disrotatory pathway is a forbidden one. The conrotatory transition state was a problem because there was no cyclic ground state reference structure with which to compare it. The accepted solution to this problem rests on an earlier study by Heilbronner (6), who examined Möbius annulenes at the Hückel level. Möbius cyclobutadiene has the structure twisted such that each p orbital is tipped 45° with respect to its neighbor. The resulting sigma skeleton and p-orbital array are pictured as structures Ia and Ib (see Methods section).

At the Hückel level, cyclobutadiene is a ground-state triplet with a π energy of 4α + 4β (4–7) and Möbius cyclobutadiene is a ground-state singlet with a π energy of 4α + 4β (6, 7). The basis for calling Möbius cyclobutadiene “aromatic” rests entirely on the fact that it is closed shell at the Hückel level. In Figure 1, the conrotatory transition state is said to be “Möbius cyclobutadiene-like” and therefore “aromatic”. The conrotatory pathway is an allowed one. In the Results and Discussion section, part A examines Heilbronner’s suggestion (6) that aromatic Möbius cyclobutadiene might be an “artifact” of Hückel theory; part B develops an aromaticity-based approach to pericyclic reactions that is independent of Möbius annulenes; and parts C and D apply that approach to selected reactions.

αN (1) = α C + βc, αN (2) = α C + 2βc, αO (1) = αC + 2βc, and α O (2) = αC + 3.2βc. PM3 computations (8) on Möbius cyclobutadiene and cyclobutadiene were carried out using the MOPAC6 program. Because Möbius cyclobutadiene is not an energy minimum, it was described by single-point calculations with (i) all CH bond lengths set at 1.07 Å, (ii) H1 in the carbon plane with both H1CC angles set at 135°, (iii) H2 and H4 45° below and above the carbon plane with all the H2CC and H4CC angles set at 120°, and (iv) H3 perpendicular to the carbon plane with both H3CC angles set at 90° (see Ia for numbering). The unrestricted Hartree-Fock (UHF) method was used for the triplet-state computations. Planar cyclobutadiene geometries were fully optimized. Results and Discussion

A. Möbius Cyclobutadiene At the Hückel level (6), Möbius cyclobutadiene Ib is nonpolar. It has a degenerate pair of HOMOs (highest occupied molecular orbitals)and a degenerate pair of LUMOs (lowest unoccupied molecular orbitals), and is expected to be a ground-state singlet. The p-orbital array in Möbius cyclobutadiene has C2 symmetry. Semiempirical calculations on Möbius cyclobutadiene include explicit consideration of the hydrogen atoms—unlike Hückel calculations, which do not. Inclusion of the hydrogen atoms in Ia imposes C1 symmetry on the structure and on the orbitals that describe it. Möbius cyclobutadiene has no π-system. It is chiral and has no C 2 axis.

Methods Zeroth order Hückel calculations were done in the usual manner, assuming the orthogonality of adjacent p orbitals. The following parameters were employed for Hückel calculations on heteroatomic systems: Figure 1. Concerted electrocyclic formation of cyclobutene.

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Figure 2. Differential orbital overlap for conrotatory and disrotatory pathways.

Single-point PM3 computations on Möbius cyclobutadiene Ia (see Methods section for details) reveal that the triplet is 35.5 kcal/mol more stable than the singlet state. It is, therefore, not a ground-state singlet. The occupied frontier orbitals of the singlet φ 9 (E = –10.59 eV) and φ10 (E = –8.60 eV) are not degenerate. The vacant frontier orbitals φ 11 (E = –2.15 eV) and φ12 (E = 0.64 eV) are not degenerate. In accord with other ground state triplet structures (see reference 9 for some examples), the singlet state for Möbius cyclobutadiene has a significant calculated dipole moment: 1.84D. When Möbius cyclobutadiene’s geometry was used to initiate a fully optimized calculation for the singlet state, the final structure was planar. Since the lowest-lying singlet state for Möbius cyclobutadiene Ia does not even correspond to a local energy minimum, it is not aromatic.

B. Transition State Modeling Without recourse to Möbius annulenes, another method must be found to analyze structures like the conrotatory transition state shown in Figure 1. Consider the stylized p-orbital drawings in Figure 2. Conrotatory motion leads to relatively little overlap in a transition state similar in structure to the starting material (10). Disrotatory motion leads to much greater orbital overlap in a transition state similar in structure to the corresponding annulene. Since (i) the lower the transition state energy, the more favored the pathway, and (ii) aromatic transition states are lower in energy than isoconjugate nonaromatic transition states that are lower in energy than isoconjugate antiaromatic transition states, the Figure 1 reactions can be analyzed as follows. Disrotatory motion leads to a “cyclobutadiene-like” transition state that is antiaromatic. Conrotatory motion leads to a “buta-

Figure 3. Concerted electrocyclic formation of cyclohexadiene.

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diene-like” transition state that is nonaromatic. Therefore, conrotatory closure is allowed and disrotatory closure is forbidden. In Figure 3, disrotatory motion leads to a “benzenelike” transition state that is aromatic. Conrotatory motion leads to a “hexatriene-like” transition state that is nonaromatic. Consequently, disrotatory closure is allowed and conrotatory closure is forbidden. At the Hückel level the notion of aromaticity is developed by means of various resonance energies (11–13) that allow for the net stabilization of the structure by all of its electrons, thus supporting a quasi-thermodynamic view of aromaticity. Alternatively, an aromatic annulene is expected to be less reactive because its frontier orbitals are remote from the nonbonding level (12), which leads to an understanding of aromaticity in terms of kinetic stability. Haddon and Fukunaga (14) have demonstrated a direct correlation between kinetic and thermodynamic stabilities for the annulenes. Thus a shift from quasi-thermodynamic to kinetic stability for aromaticity-based classifications of monocyclic transition states would not alter any existing orbital symmetry analyses. However, the more modern and powerful (15) kinetic stability–based arguments are superior to resonance energy–based arguments for reactions involving polycyclic transition states (see section D). Further analyses exploit expected orbital-overlap differences in transition states and appeal to kinetic stability–based aromaticity arguments. Reactions that are thermally forbidden are presumed to be photochemically allowed for reasons advanced earlier (3).

C. Analysis of Selected Reactions: Monocyclic Transition States In general, reference structures are generated for even transition states in the following way: a partially formed/broken bond (no node) is replaced by a double bond and a partially formed/broken antibond (node) is replaced by no bond. Analysis is simplified if transition states are routinely depicted with the fewest possible nodes. All reactions considered in this section have monocyclic transition states and can be conveniently assessed using Hückel’s rule. Electrocyclic reactions have been exemplified in Figures 1 and 3 and discussed in the previous section. A cycloaddition reaction is shown in Figure 4. The π4s + π2s addition produces a “benzene-like” aromatic transition state. The π 4 s + π 2 a addition gives a

Figure 4. Concerted formation of cyclohexene: Diels-Alder pathways.

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Figure 7. Forbidden conversion of Dewar benzene into benzene.

Figure 5. Suprafacial and antarafacial sigmatropic rearrangement pathways.

Figure 8. Concerted thermolysis of cyclooctatetraene.

“hexatriene-like” nonaromatic transition state. The former reaction is allowed and the latter forbidden. In addition to the usual treatment of new bonding/ antibonding interactions to generate reference structures for sigmatropic rearrangements in hydrocarbons, the migrating group and the sp3 center it migrates from are replaced by a vinyl group. Figure 5 presents a simple sigmatropic rearrangement. Suprafacial migration ( π 2 s + σ 2 s) gives rise to a transition state that is “cyclobutadiene-like” and therefore antiaromatic. Antarafacial migration ( π2 a + σ2 s) gives rise to a transition state that is “butadiene-like” and therefore nonaromatic. Suprafacial migration is forbidden and antarafacial migration is allowed. Physically unachievable antarafacial migration along with symmetry-forbidden suprafacial migration suffice to explain the otherwise surprising gas-phase stability of enols. Cheletropic expulsions usually go through odd transition states. Reference structures may be generated for odd transition states by replacing the docking/departing group with a methine carbon (or with a single heteroatom) having the appropriate number of π electrons. Thus in Figure 6, the transition state for linear expulsion is isoconjugate with the cyclopropenyl anion (antiaromatic) and the transition state for nonlinear expulsion is isoconjugate with the cyclopropenyl cation (aromatic). Therefore, nonlinear expulsion is allowed and linear expulsion is forbidden.

they are monocyclic. Thus the disrotatory thermal opening of Dewar benzene (see Figure 7) would furnish benzene through a transition state which might be classed as antiaromatic on the grounds that it has a cyclobutadiene ring (see structure II for a monocyclic depiction of the transition state). In some cases this simplification leads to ambiguity. The thermal closure of cyclooctatetraene (see Figure 8) is expected to be allowed in either fashion, since disrotatory closure leads to an aromatic benzene-like porbital array and conrotatory closure leads to an aromatic Möbius cyclobutadiene-like p-orbital array. Furthermore, Figure 9 is erroneously expected to lead to suprafacial addition through a benzene-like transition state (see structure III for a monocyclic depiction of the suprafacial transition state).

D. Analyses of Selected Reactions: Polycyclic Transition States In order to exploit Hückel’s rule in the analyses of transition states for pericyclic reactions, it is common practice to treat polycyclic transition states as though

Figure 6. Concerted linear and non-linear cheletropic expulsions.

The present approach to polycyclic transition states will generate reference structures as outlined earlier. In general, it will be necessary to carry out simple Hückel

Figure 9. Concerted cycloaddition to heptafulvalene.


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Figure 10. Forbidden isomerization of methylene cyclohexadiene.

Figure 11. A polycyclic cheletropic expulsion.

Figure 12. A photochemical Diels-Alder reaction.

calculations on those reference structures. From the Hückel results one can obtain the ∂EFMO, which is the energy difference between the eigenvalues of the frontier molecular orbitals (EHOMO – ELUMO or ESOMO – ESOMO) for each reference structure. The thermolysis depicted in Figure 7 would now lead to a disrotatory transition state analogous to the non-aromatic bicycle IV and a conrotatory transition state analogous to benzene V. Thus the surprising stability of Dewar benzene (16) (t 1/2 = 2 days) can be attributed to forbidden disrotatory opening. The electrocyclic thermolysis presented in Figure 8 would lead to a disrotatory transition state analogous to the bicycle VI and a conrotatory transition state analogous to the antiaromatic monocycle VII. The known predilection for disrotatory closure (17) is thus rationalized.

Figure 10 presents a representative bicyclic sigmatropic rearrangement. Suprafacial [1,3] migration would go through a transition state analogous to benzocyclobutadiene X, while physically impossible antarafacial [1,3] migration would go through a transition state analogous to the monocycle XI. Consistent with experiment (18), an analysis using ∂EFMO values leads to the conclusion that suprafacial migration is forbidden. In many cases aromaticity arguments based on total Hückel π-energies directly or on resonance energies of various kinds lead to the same conclusion as a kinetic stability–based argument. However, in the Figure 10 reaction, a quasithermodynamic analysis using Hückel πenergies leads to a conclusion that is inconsistent with experiment (see structures X and XI for Eπ numbers).

A representative polycyclic cheletropic expulsion (19) is depicted in Figure 11. Disrotatory linear expulsion through a transition state analogous to XII is allowed, whereas conrotatory linear expulsion through a transition state analogous to XIII is forbidden. Finally, consider the well-known photochemical Diels-Alder reaction (reference 1, page 79) shown in Figure 12. A [π4 s + π2s] process would go through a transition state analogous to XIV, whereas a [π4s + π2a] process would go through a transition state analogous to XV. A [π4s + π2a] process would be thermally forbidden and photochemically allowed.

The cycloaddition shown in Figure 9 would lead to a suprafacial transition state analogous to the tricycle VIII and an antarafacial transition state analogous to the vinyl-substituted bicycle IX. A kinetic stability–based assessment of transition state aromaticity leads to the expectation that suprafacial addition should be forbidden and antarafacial addition allowed. That cycloaddition is known to proceed in an antarafacial manner (see reference 1, page 85). 902

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E. Conclusions The anti-intuitive concept of “aromatic” Möbius cyclobutadiene is an artifact of Hückel theory. Using kinetic stability as a basis for aromatic character, transition states can be classified aromatic, nonaromatic or antiaromatic leading to unambiguous assignments of allowed or forbidden for pericyclic reactions. This view of pericyclic transition states avoids the principal pedagogical obstacle for students of these reactions: aromatic Möbius annulenes. Literature Cited 1. Woodward, R. B.; Hoffmann, R. The Conservation of Orbital Symmetry; Verlag Chemie: Weinheim, 1970.

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

Fukui, K. Acc. Chem. Res. 1971, 4, 57. Dewar, M. J. S. Angew. Chem. (Int. Ed. Engl.) 1971, 10, 761. Zimmerman, H. E. Acc. Chem. Res. 1971, 4, 272. Zimmerman, H. E. Tetrahedron 1982, 38, 753 and references therein. Heilbronner, E. Tetrahedron Lett. 1964, 1923. Zimmerman, H.E. In Pericyclic Reactions; Marchand, A. P.; Lehr, R. E., Eds.; Vol. 1; Academic: New York, 1977. Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209. Langler, R. F.; Ginsburg, J. L.; Snooks, R.; Boyd, R. J. J. Phys. Org. Chem. 1991, 4, 566. Dewar, M. J. S.; Ramsden, C. A. J. Chem. Soc., Perkin 1, 1974, 1840. Liberles, A. Introduction to Molecular-Orbital Theory; Holt, Rinehart and Winston: New York, 1966. Durkin, K. A.; Langler, R. F. J. Phys. Chem. 1987, 91, 2422. (a) Trinajstic, N. Chemical Graph Theory; CRC: Boca Raton, FL, 1983; Vol. 2 p 1; (b) Langler, R. F. Aust. J. Chem. 1991, 44, 297. Haddon, R. C.; Fukunaga, T. Tetrahedron Lett. 1980, 21, 1191. Zhou, Z.; Parr, R. G. J. Am. Chem. Soc. 1989, 111, 7371. Volger, H. C.; Hogeveen, H. Rec. Trav. Chim. Pays-Bas 1967, 86, 830. Huisgen, R.; Mietzsch, F. Angew. Chem. (Int. Ed. Engl.) 1964, 3, 83. Bailey, W. J.; Baylouny, R. A. J. Org. Chem. 1962, 27, 3476. Carpino, L. A. Chem. Commun. 1966, 494.


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A Conceptually Simple Approach to the Analysis of Aromaticity in

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