The Aromaticity of Pericyclic Reaction Transition States

Research: Science and Education

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The Aromaticity of Pericyclic Reaction Transition States Henry S. Rzepa Department of Chemistry, Imperial College London, South Kensington Campus, Exhibition Road, London, SW7 2AY, United Kingdom; [email protected]

The electronic theory of organic chemistry underpins one of the most interesting, but subtle, concepts currently taught in the subject, that of the “stereoelectronic control” of reactions. For a particular mechanistic type known as the pericyclic reaction, other concepts fundamental to organic chemistry such as stereochemistry, chirality, aromaticity, and quantum mechanics are interwoven. The impact of this fusion of ideas on organic chemistry has been recognized with the award of a Nobel Prize in 1981 to one the original architects, Roald Hoffmann (the other, Robert Woodward, had died in 1979 and was ineligible to receive the prize posthumously). In this article, these diverse concepts are brought together via an illustration of transition states for one specific pericyclic reaction that played a key role in the first experimental synthesis of a new type of molecule, a Möbius annulene. The discoverer of the electron, J. J. Thomson, was among the first to also develop models using the electron to account for chemical bonding. In 1921, just before the dawn of quantum mechanics, he published (1) an exploration of the bonding for the archetypal aromatic molecule, benzene. In his scheme, each C⫺C region in this species was bonded using three electrons (Figure 1). Reading his description, it is evident that the electron was still very much regarded as a point particle and that there was yet hardly a glimmer of recognition that the group of three electrons might have differing spatial (3D) characteristics. The advent of quantum mechanics and the formulation of the Schrödinger wave equation brought with it an understanding of the spatial and energetic properties of electrons, more formally described by wavefunctions. This allowed a segregation of two of Thomson’s three electrons in each C⫺C region of benzene into a low energy σ set, which form what is now called a C⫺C σ bond, and the third electron as contributing to a spatially distinct band of six rather higher-energy electrons not directly associated with any single C⫺C bond but with the aromatic ring itself, and which became widely known as the aromatic π sextet (Figure 1) (2).

Figure 1. (left) Thomson’s three-electron bonds in benzene and (right) the segregation of these 18 electrons into six pairs of two-electron C⫺C bonds and a π aromatic sextet following Hückel.

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The first person to formalize this separation was Erich Hückel in 1930 (3). He used the new theory of quantum mechanics to derive a principle of σ–π separability, which he used to explain the restricted rotation in alkenes. Hückel in 1931 extended this concept to benzene, predicting particular stability for a cyclic arrangement of six π electrons in wavefunctions (molecular orbitals) formed by overlapping carbon-centered 2p atomic orbitals into a planar ring. The concept of atomic orbitals had previously been derived by solving the quantum mechanical Schrödinger wave equation for a hydrogen atom. It took little while longer for organic chemists to properly generalize and understand Hückel theory as a useful, albeit approximate, theoretical basis for the wider concept of aromaticity. The emergent Hückel rule (first succinctly coined not by Hückel himself but by William Doering as late as 1951; ref 3) is conventionally applied to planar molecules containing cyclically conjugated π electrons (referred to below as having Hückel topology) and is now enumerated: 1. 4n + 2 (where n is an integer) π electrons, thermally (closed shell with all molecular orbitals doubly occupied) aromatic and stable 2. 4n π electrons, photochemically (open shell, with two molecular orbitals each occupied by a single electron) aromatic and stable 3. 4n π electrons, thermally anti-aromatic and less stable 4. 4n + 2 π electrons, photochemically anti-aromatic and less stable.

Rules 2 and 4 were added in the 1960s, as the quantum mechanical understanding of photochemically excited states (open shell systems with two molecular orbitals each singly occupied) developed. These nowadays are regarded as a much more approximate heuristics than the thermal rules 1 and 3. A particularly characteristic feature of what might be called “classical” aromatic chemistry is the planarity (two-dimensionality) of the ring. When the representation of a planar molecule is reflected in a mirror, the 3D arrangement of atoms can be exactly superimposed on the original unreflected set, such molecules are said to be achiral. A small class of aromatic molecules are forced to be nonplanar for steric reasons. A good example are the helicenes, which adopt a helical arrangement of the rings (Figure 2). When reflected in a mirror plane such a helicene cannot be superimposed upon the original and the system is said to exist as a pair of chiral or dissymmetric enantiomers. Of course, aromatic molecules can support chiral groups as substituents on the rings, but we exclude this class in our argument here, since we are concerned only with the nature of the aromatic structures themselves.

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Hückel and Möbius Aromatics

Figure 2. A heptahelicene and its non-superimposable mirror image.

Figure 3. Heilbronner’s suggestion for a π Möbius conjugated system obtained by π electrons located in molecular orbitals resulting from 2p atomic orbitals distributed around a Möbius strip bearing a single half-twist, rather than a planar Hückel ring bearing no twist in the orbital basis.

Thus these two great concepts of organic chemistry, aromaticity and chirality, remained mostly exclusive. Edgar Heilbronner in 1964 (4) and Howard Zimmerman in 1966 (5) both came up with radical new suggestions that allow a fusion of these concepts. Rather than distributing π electrons in a planar ring comprising precisely parallel overlap of 2p atomic orbitals, Heilbronner considered what might happen if this array were instead distributed along a Möbius strip bearing a single half (left or right) twist (Figure 3). Heilbronner applied Hückel’s equations (3) to such a cyclic Möbius ring, finding that a 4n π-electron system would be a closed-shell species like benzene, with no loss of π-electron resonance energy compared to the equivalent untwisted Hückel ring. A closed-shell 4n + 2 π electron Möbius ring was predicted to be less stable than the untwisted Hückel counterpart. Like Hückel before him, Heilbronner did not derive a succinct rule of aromatic stability from these results. Zimmerman (5) was the first to clearly associate the π-electron stability of such Möbius rings with an inversion of the aromaticity rules 1 and 2 above. Specifically, populations of 4n π electrons result in closed-shell (two electrons per π energy level) molecules if the 2p atomic orbitals are distributed along a Möbius strip (rule 1 inverted), whereas 4n + 2 πelectrons will adopt an open-shell (photochemical) distribution in which two of the electrons will now each occupy a separate molecular orbital (rule 2 inverted) (5). By adding a corollary for the anti-aromatic cases, rules 5–8 to complement 1–4 can be listed: 5. 4n electrons, thermally (closed shell) aromatic and stable with Möbius π topology 6. 4n + 2 electrons, photochemically (open shell) aromatic and stable with Möbius π topology 7. 4n + 2 electrons, thermally (closed shell) less stable with Möbius π topology 8. 4n π electrons, photochemically (open shell) less stable with Möbius π topology.

Figure 4. Frost–Musulin and Zimmerman mnemonics for aromaticity selection rules. A six-sided polygon is shown for the Hückel case to coincide with the example shown later in Scheme III (solid arrows) and an eight-sided polygon is shown for the Möbius case to coincide with the dashed arrows in Scheme III.

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A useful visual mnemonic first proposed by Frost and Musulin (6) for orbital energies of π-electron rings based on inscribing a polygon with one vertex down for the Hückel rules, was memorably extended by Zimmerman (5) to Möbius systems by redrawing the polygons with one edge down (Figure 4). Another aspect of Möbius systems that was not directly commented upon by Heilbronner is that a Möbius strip bearing one half-twist is also chiral, in the sense noted above for the heptahelicene molecule (Figure 2). An ideal Möbius strip has only a C2 axis of symmetry present. The specific absence of a plane of symmetry means the mirror image of a Möbius strip is not superimposable upon the original. In contrast, an ideal planar aromatic molecule of the Hückel type does have at least one plane of symmetry, referred to here as a Cs mirror plane, which means that its mirror image is superimposable with the original. Thus in Möbius ringed molecules, we do now have a fusion of two seminal concepts in organic chemistry, that of aromaticity and of chirality!


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Quantifying Aromaticity

Scheme I. An example from Woodward and Hoffmann illustrating how the outcome of a pericyclic reaction depends on stereoelectronic control mediated by heat or by light (7).

The next intellectual leap involves a class of organic reactions known as pericyclic and the recognition by Woodward and Hoffmann (7) that the stereochemical outcome of such reactions was quantum mechanical in origin (Scheme I). The original Woodward and Hoffmann argument was based on the symmetries of a subset of the molecular orbitals called frontier orbitals. This analysis was extended by Longuet-Higgins and Abrahamson (7) to a more formal diagram showing the correlation of the symmetries of the reactants and product molecular orbitals and particularly whether either of the C2 or the Cs symmetry elements noted above were preserved during the course of the pericyclic reaction. A difficulty in applying such symmetry arguments was the experimental observation that most pericyclic reactions involved no formal symmetry at all! This difficulty can be overcome by the following procedure: • By considering only the (cyclic) transition state for the pericyclic reaction, one can pose the question: is it aromatic or not? The advantage is that the aromaticity of a system is robust to minor, desymmetrizing perturbations caused by the presence of substituents and other nonparticipating groups. • By equating (ideal) C2 transition-state symmetry with Möbius topology and (ideal) Cs symmetry with Hückel topology, one can now apply the aromaticity rules listed above to the transition state.

The first person to associate the π-electron stability (aromaticity) of Möbius and Hückel rings with the “allowed” or “forbidden” nature of the transition states for pericyclic reactions was Zimmerman (5), via the mnemonic shown above (Figure 4). Thus the preferred outcome of a pericyclic reaction can be predicted by analyzing whether the transition state might exhibit Hückel or Möbius aromaticity (7). This simple statement carries some of the most profound and powerful concepts in modern organic chemistry. www.JCE.DivCHED.org

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Before introducing a pericyclic reaction that can be used to embody and illustrate these concepts, one more tool is needed. How does one quantify, or measure, the concept known as “aromaticity”. Although much of the discussion above is couched in terms of the (theoretical) π-electron energy, it turns out that accurate measures of aromaticity in terms of (theoretical or experimental) energies are frustratingly elusive. Many other criteria have been proposed, and the consensus seems to be that no single experimental measurement or theoretical calculation can fully, accurately, and uniquely represent aromaticity. It is also evident that experimentally measuring aromaticity for a transition state will be particularly difficult given its very short lifetime (∼10᎑15 s)! Instead, recourse has to be taken to a quantum mechanical calculation rather than direct measurement. Instead of using energies, two other property calculations are used here for this purpose: 1. The first is inspection of the C⫺C (or C⫺heteroatom) bond lengths around the periphery of the ring formed by the pericyclic transition state. For relatively small sized rings (less than 14 carbon atoms), aromaticity can be related to the degree of alternation in the bond lengths; no alternation indicates a high degree of aromaticity (and implied stability), whereas partitioning into short (double) and long (single) bond lengths indicates no aromaticity or even anti-aromaticity. This measure is often expressed as ∆r, the difference between the longest and the shortest C⫺C bond in the cycle, which typically has a value between 0.00 and 0.04 Å for an aromatic ring and equal to 0.1 Å for a nonaromatic or anti-aromatic ring. 2. The second measure was introduced by Paul Schleyer (8) and was based on the predicted magnetic properties of the ring current induced by aromatic electrons. One measurable property of aromatic molecules is the NMR chemical shift of, for example, protons exposed to such ring currents, which have values characteristic of “aromaticity” (7–8 ppm relative to tetramethylsilane). To produce a more specific, single metric of aromaticity, Schleyer proposed instead a calculated property he termed the nucleus independent chemical shift or NICS(0). This property was to be computed at the center of the ring whose aromaticity needed to be estimated. By comparison with benzene, a value of about ᎑10 ppm would be deemed aromatic, a value of around zero would be non-aromatic, while a positive value of , for example, +20 would be deemed anti-aromatic. Both these metrics will be used in discussing the example introduced below.

Electrocyclic Ring-Closing Reaction and the Synthesis of a [16] Möbius Annulene The example we have chosen is derived from a remarkable recent synthesis inspired by Heilbronner’s 1964 proposal. From rule 5 above, one can see that a 4n cyclic aromatic (or annulene) is predicted to be Möbius aromatic. Herges (9) and colleagues Ajami, Oeckler, and Simon set out to synthesize a


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Scheme II. Herges’ scheme for the synthesis of a [16] Möbius ring. Bonds marked with b carry a benzo substituent, omitted for clarity. Isomer F with a C2 symmetry axis is the first known Möbius annulene. Note that either the solid or dashed arrows are used in E to form the resonance structures of F.

[16] Möbius annulene (n = 4) in the laboratory with the purpose of subjecting it to experimental tests to see whether it really were aromatic. The synthetic route is presented in Scheme II and involves a series of consecutive pericyclic reactions. Herges was able to isolate the intermediates E, and when subjected to light, these formed a mixture from which was isolated one specific product. X-ray crystallography showed that this isomer had the C2 axis of symmetry required of a Möbius annulene. This synthesis was set as a problem in an undergraduate class associated with a course on pericyclic reaction given by the author, and the students were invited to “push arrows” illustrating the mechanism, the total number of arrows for each step then being used to derive which of the 4n(4n + 2) rules listed above is applicable for that step. One characteristic feature of pericyclic problems is that often, two or more alternatives to the arrow pushing can be proposed, and normally these alternatives all result in the same analysis of the overall reaction step. So although it was no surprise that the majority of students in the class illustrated step E to F with the solid arrows (examples of such reactions were contained in the lecture notes for the course), a significant number of students instead chose to use the dashed arrows for this step. The stereochemistry at the bicyclic ring junction in E had been left undefined in the question, in the hope of provoking the students (and the present author!) to think about the implications. A tutorial, in which this problem and possible answers to it were discussed with students, soon revealed that those students who had invoked the solid arrows were led to analyzing the consequences of a 4n + 2 rule (n = 1), while those who had used the dashed arrows were obliged to use the 4n rule (n = 3) for this electrocyclic ring-opening reaction. It 1538


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seemed that for either route, one could regard the reaction as simultaneously following one rule and breaking the other, and that a contradiction seemed to exist. This certainly led to a lively tutorial. [12] Annulene as a Model Further thought reveals that this specific example can be used to concisely encapsulate many of the concepts required to fully understand pericyclic reactions. To illustrate these, a reasonably accurate quantum mechanical model of the two possible transition states for this reaction was computed and is analyzed in detail below. Several simplifications of the system were undertaken to enable a practical model to be constructed: 1. The size of the annulene was reduced from [16] to [12] (Scheme III), making it conformationally much less complex. This exact reaction is actually known, albeit proceeding in the reverse direction (10). 2. The reaction rate can be increased by either light (as in Herges’ synthesis) or by heat (9). The theoretical models were computed for the latter, as exploring the photochemical potential surface is a far more complex task, with results that may be expected go well beyond the conventional Woodward–Hoffmann approach. 3. Also noteworthy is a fascinating article (11) describing the cis–trans isomerization in the [12] annulene shown in Scheme III as also involving a Möbius transition state.

Two transition states were located for the ring opening reaction. This was done at a level of theory summarized as B3LYP/6-31G(d), which means use of a density functional


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these transition states will be discussed individually: • The Cs plane and C2 axis of symmetry should be clearly evident from the two geometries. Each vibrational mode reflects this symmetry. • The stereochemistry of each reaction also reflects its symmetry. The system with Cs has cis stereochemistry at the bicyclic ring junction, while that with C2 symmetry has trans stereochemistry.

Scheme III. A simplified model electrocyclic reaction, showing the plane (Cs ) or axis (C2) of symmetry which can be preserved during reaction. Note the either the solid or dashed arrows could be used to open the ring.

• The Cs system is said to have the two termini of the bond cleaving or forming rotation in opposite directions, (one clockwise, the other anti-clockwise), a process known as disrotation. The C2 system rotates both termini in the same direction, that is, conrotation. • The Cs system forms or cleaves the C⫺C bond from the same face of the π system located on the six-membered ring, described as suprafacial bond formation– cleavage. The C2 system forms or cleaves the C⫺C from the top face of one end of the eight-membered ring and the bottom face of the other end, described as antarafacial bond formation–cleavage. • An even more concise summary of these definitions is to refer to the transition state with Cs symmetry as having Hückel form, and to that with C2 symmetry as having Möbius form.

Figure 5. Geometries and transition normal modes for electrocyclic ring opening shown in Scheme III for transition states with Cs and with C2 symmetry. The latter shows the same helical features as previously illustrated in Figure 2. The Supplemental MaterialW contains 3D rotatable models that can be viewed instead (Java must be installed on your system to enable this).

procedure with an orbital basis set for the atoms known as 6-31G(d). This combination is frequently employed nowadays and its properties are well understood. The first transition state in fact corresponds to the three solid arrows, maps to the 4n + 2 rule, and hence is deemed to correspond to a Hückel type in which a plane of symmetry (Cs) is maintained throughout the reaction. This implies that the six-membered ring formed by the transition state is Hückel aromatic (rule 1 above). The second transition state corresponds to the four dashed arrows, maps to the 4n rule, and implies that the eight-membered transition ring has C2 symmetry and is Möbius aromatic (rule 5 above). Are these properties are reflected in the two quantitative measures of aromaticity described above? Shown in Figure 5 are 3D models visualized using the Jmol applet (12) illustrating the calculated geometries of the two transition states. The model is animated to illustrate the form of the reaction mode (see the Supplemental MaterialW). The vibrational mode is computed from a full vibrational analysis of the system and shows in each case the central C⫺C bond periodically breaking or making, in one direction leading to the monocyclic [12] annulene and in the other direction to the bicyclic starting material. Various properties of www.JCE.DivCHED.org

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• With the Cs system, the C⫺C bond lengths around the six-membered (putatively aromatic) ring, starting with the breaking C⫺C bond, are 2.22, 1.425, 1.38, 1.42, 1.38, and 1.425 Å. This pattern shows only a little deviation from the mean of about 1.40 Å, which is typical of the length in benzene itself. Omitting the actual forming or cleaving bond itself, ∆r = 0.04 Å. Much greater alternation is seen in the values going around the eight-membered ring: 2.22, 1.46, 1.35, 1.48, 1.34, 1.48, 1.35, and 1.46 (∆r = 0.14 Å) and these values are more typical of the non-aromatic cyclooctatetraene ring. A further feature is that the six-membered ring is almost planar, while the eight-membered ring is highly buckled. These geometries clearly indicate that for the Cs isomer, the six-membered ring is clearly aromatic in accord with the supposition first suggested above. • In contrast, the values for the six-membered ring in the C2 system are 2.37, 1.48, 1.35, 1.47, 1.35 and 1.48, (∆r = 0.13 Å). This alternating pattern is much reduced for the eight-membered ring: 2.37, 1.38, 1.42, 1.39, 1.43, 1.39, 1.42, and 1.38 (∆r = 0.04 Å). The former is clearly non-aromatic while the latter is aromatic. In addition, the helical nature of the eight-membered ring can be perceived if compared to that of the helicene shown in Figure 2. • The Cs system has a NICS(0) index of ᎑11.1 ppm at the centroid of the six-membered ring and +0.3 for the eight-membered ring. Bearing in mind a value of about ᎑10.0 for benzene, this clearly shows the smaller ring as the aromatic one. • The C2 system has a NICS(0) index of +2.5 for the six-membered ring and ᎑9.5 for the eight-membered ring, again clearly showing the larger ring now is the aromatic one.


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These various measures of aromaticity clearly illustrate how the concept can be applied to transition states for pericyclic reactions. It also enables one to reconcile how a reaction can apparently both follow one rule but break the other in this hybrid electrocyclic reaction. The answer is that only one ring is aromatic in each case, while the other ring essentially just spectates as a non-aromatic participant. In effect, stabilization due to cyclic π conjugation occurs only in the aromatic ring, while the spectating ring retains conventional unconjugated bonds. For those interested in pursuing this topic, an extension of the reaction in Scheme III to one with two equal-sized rings is presented in the digital interactive version of this article (see the Supplemental MaterialW). Conclusions Chemical reactivity is a complex process, controlled by a variety of influences. Pericyclic reactions are a class that also often exhibit highly stereospecific behavior and that are now understood to be subject to quite clear stereoelectronic influences. These in turn can be traced back to quite simple derivations of the Schrödinger wave equation and related to another concept known as aromaticity. To do so fully, requires an understanding of selection rules expressed in terms of two different forms of aromatic species, the ubiquitous planar Hückel aromatic and the relatively new type of Möbius aromatic. In illustrating the first synthesis of such a stable Möbius system, we uncover one step in the sequence where the mechanism can be explained in terms of either Hückel or of Möbius aromaticity of the transition state for the reaction. This exposes a very rare example of a pericyclic reaction that at first sight appears to simultaneously obey one selection rule and to disobey another. Reconciling this apparent discrepancy requires a deeper understanding of how aromaticity as a concept can be applied to such reactions. WSupplemental

Material

A digital version of this article with interactive figures is available in this issue of JCE Online.

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Literature Cited 1. Thomson, J. J. Philosophical Magazine 1921, 41, 510–538. 2. Writing prior to the discovery of the electron in 1897, Henry Armstrong was the first to give a description of benzene (and naphthalene) that is recognizable in all regards as encapsulating the modern concept of an aromatic π-electron sextet and its more general 4n + 2 form. Armstrong, H. E. Proc. Chem. Soc. 1890, 101–105. Ernest Crocker is now recognized as the first to produce a modern more general description for organic chemistry: Crocker, E. C. J. Am. Chem. Soc. 1922, 44, 1618– 1630. For a review, see Balaban, A. T.; Schleyer, P. v. R.; Rzepa, H. S. Chem. Rev. 2005, 105, 3436–3447. 3. (a) Hückel, E. Z. Physik 1930, 60, 423. Hückel, E. Z. Phys. 1931, 70, 204–86. (b) Doering, W. von; Detert, F. J. Am. Chem. Soc. 1951, 73, 876–877. 4. Heilbronner, E. Tetrahedron Lett. 1964, 1923–1928. For a generalization of Heilbronner’s derivation for Möbius systems bearing one half twist to those bearing n half twists, see Fowler, P. W.; Rzepa, H. S. Phys. Chem. Chem. Phys. 2006, 1775–1777. 5. Zimmerman, H. E. J. Am. Chem. Soc. 1966, 88, 1564. Zimmerman, H. E. Tetrahedron 1982, 38, 753–758. 6. Frost, A.; Musulin, B. J. Chem. Phys. 1953, 21, 572. 7. (a) Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87, 395–397. (b) Longuet-Higgins, H. C.; Abrahamson, E. W. J. Am. Chem. Soc. 1965, 87, 2046. (c) Zimmerman, H. E. Accounts Chem Res. 1971, 4, 272. (d) Dewar, M. J. S. Angewandte Chemie, Int. Ed. 1971, 10, 761–776. 8. Schleyer, P. von R.; Maerker, C.; Dransfeld, A.; Jiao, H.; van Eikema Hommes, N. J. R. J. Am. Chem. Soc. 1996, 118, 6317–6318. 9. Ajami, D.; Oeckler, O.; Simon, A.; Herges, R. Nature 2003, 426, 819–821. 10. (a) Oth, J. F. M.; Röttele, H.; Schröder, G. Tetrahedron Lett. 1970, 61. (b) Oth, J. F. M. Pure Appl. Chem. 1971, 25, 573. 11. Castro, C.; Karney, W. L.; Valencia, M. A.; Vu, C. M. H.; Pemberton, R. P. J. Am. Chem. Soc. 2005, 127, 9704–9705. 12. The Jmol applet is available from http://jmol.sourceforge.net/ (accessed Jun 2007).


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The Aromaticity of Pericyclic Reaction Transition States

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