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Woodward–Hoffmann rules

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The Woodward–Hoffmann rules devised by Robert Burns Woodward and Roald Hoffmann are a set of rules in organic chemistry predicting the stereochemistry of pericyclic reactions based on orbital symmetry. These include electrocyclic reactions, cycloadditions (including cheletropic reactions), sigmatropic reactions, and group transfer reactions. Hoffmann was awarded the 1981 Nobel Prize in Chemistry for this work, shared with Kenichi Fukui who developed a similar model; since Woodward had died two years before, he was not eligible to win what would have been his second Nobel Prize for Chemistry.

Electrocyclic reaction

The rules apply to the observed stereospecificity of electrocyclic ring-opening and ring-closing reactions at the termini of open chain conjugated polyenes either by application of heat (thermal reactions) or application of light (photochemical reactions). In the original publication in 1965,[1] three rules are stated as:

  • In open systems containing 4n + 2 electrons, terminal bonding interaction within ground-state molecules requires overlap of orbital envelopes on the same face of the system, attainable only by disrotatory displacements.

Organic reactions that obey these rules are said to be symmetry allowed. Reactions that take the opposite course are symmetry forbidden and require a lot more energy to take place if they take place at all.

The rules predict the outcome of several ground-state reactions:

Cyclopropyl cation → allyl cation: disrotatory
Cyclopropyl radical → allyl radical: conrotatory
Cyclopropyl anion → allyl anion: conrotatory
Cyclopentenyl cation → pentadienyl cation: conrotatory

The stated rules are supported by theoretical calculations using the extended Hückel theory. For example, the activation energy required for thermal ring closing reaction of butadiene can be calculated as a function of the C-C-C bond angles keeping the other variables constant. Angles larger than 117° show a slight preference for a disrotatory reaction but with smaller angles a conrotatory reaction mode is preferred.

One year after the Woodward-Hoffmann publication, publications describing an alternative theoretical approach based on the parity of nodes around a cyclic array of basis orbitals was described [2][3]

A recent paper describes how mechanical stress can be used to reshape chemical reaction pathways to lead to products that apparently violate Woodward–Hoffman rules.[4]

General Formulation

Though the Woodward–Hoffmann rules were first stated in terms of electrocyclic processes, they were soon generalized to all pericyclic reactions. In the generalized Woodward-Hoffmann rules the more inclusive bond topology descriptors antarafacial and suprafacial subsume the terms conrotatory and disrotatory, respectively. Antarafacial refers to bond making or breaking through the opposite face of a π system, p orbital, or σ bond, while suprafacial refers to the process occurring through the same face. The general statement, as given in Woodward and Hoffmann's 1969 review is as follows:

A ground-state pericyclic change is symmetry-allowed when the total number of (4q+2)s and (4r)a components is odd.[5]

Here, (4q+2)s and (4r)a refer to suprafacial (4q+2)-electron and antarafacial (4r)-electron components, respectively. Alternatively, the general statement can be formulated as

A pericyclic reaction involving 4n+2 or 4n electrons is thermally allowed if the number of antarafacial components is even or odd, respectively.

Interestingly, this requirement stated in 1969 and 1970 is seen to be equivalent to the 1966 Möbius-Hückel concept treatment of Zimmerman.[2][3] Thus each (4r)a component has a plus-minus sign inversion. With an odd number of these one has a Möbius cycle.With an even number one has a Hückel cycle. The Möbius systems require 4N electrons and the Hückel systems need 4N+2 electrons for allowedness. Yet the equivalency of the Möbius-Hückel concept was not cited in these Woodward-Hoffmann papers.

In other words, a pericyclic reaction is allowed if the sum of the number of electron pairs involved and number of antarafacial components is odd. For example, the Diels-Alder reaction involves an odd number of electron pairs (3 pairs of electrons, 2 pairs from the diene and 1 pair from the dienophile) and 0 antarafacial components (since there are 2 components and both are suprafacial). The conrotatory 4π thermal electrocyclization involves an even number of electron pairs (2 pairs) and 1 antarafacial component. Both reactions described above are thermally allowed processes. In practice, an even number of antarafacial components almost always means zero components, and an odd number almost always means one component, as transition states involving two or more antarafacial components are generally too strained to be feasible. Note that in this formulation, the electron count refers to the entire reacting system, rather than to individual components in Woodward and Hoffmann's original statement.

A pericyclic reaction in which these (equivalent) conditions are not satisfied is thermally forbidden. In general, reactions that are thermally forbidden are photochemically allowed, and vice versa.

Controversy

It has been stated that the chemist E. J. Corey, also a Nobel Prize winner, feels he is responsible for the ideas that laid the foundation for this research, and that Woodward unfairly neglected to credit him in the discovery. In a 2004 memoir published in the Journal of Organic Chemistry,[6] Corey makes his claim to priority of the idea: On May 4, 1964, I suggested to my colleague R. B. Woodward a simple explanation involving the symmetry of the perturbed (HOMO) molecular orbitals for the stereoselective cyclobutene to 1,3-butadiene and 1,3,5-hexatriene to cyclohexadiene conversions that provided the basis for the further development of these ideas into what became known as the Woodward–Hoffmann rules.

Corey, then 35, was working into the evening on Monday, May 4, as he and the other driven chemists often did. At about 8:30 p.m., he dropped by Woodward's office, and Woodward posed a question about how to predict the type of ring a chain of atoms would form. After some discussion, Corey proposed that the configuration of electrons governed the course of the reaction. Woodward insisted the solution wouldn't work, but Corey left drawings in the office, sure that he was on to something.[7]

I felt that this was going to be a really interesting development and was looking forward to some sort of joint undertaking," he wrote. But the next day, Woodward flew into Corey's office as he and a colleague were leaving for lunch and presented Corey's idea as his own -- and then left. Corey was stunned.

In a 2004 rebuttal published in the Angewandte Chemie,[8] Roald Hoffmann denied the claim: he quotes Woodward from a lecture given in 1966 saying: I REMEMBER very clearly—and it still surprises me somewhat—that the crucial flash of enlightenment came to me in algebraic, rather than in pictorial or geometric form. Out of the blue, it occurred to me that the coefficients of the terminal terms in the mathematical expression representing the highest occupied molecular orbital of butadiene were of opposite sign, while those of the corresponding expression for hexatriene possessed the same sign. From here it was but a short step to the geometric, and more obviously chemically relevant, view that in the internal cyclisation of a diene, the top face of one terminal atom should attack the bottom face of the other, while in the triene case, the formation of a new bond should involve the top (or pari passu, the bottom) faces of both terminal atoms.

In addition, Hoffmann points out that in 2 publications from 1963[9] and 1965,[10] Corey described a total synthesis of the compound dihydrocostunolide. Although in it an electrocyclic reaction is described, Corey has nothing to offer with respect to explaining its stereospecifity. Further, it is noteworthy that Corey said nothing of his so-called idea for nearly 2 decades after Woodward's death.

Electrocyclic reaction step in 1963 Corey synthesis of Dihydrocostunolide

This photochemical reaction involving 4*1+2 electrons is now recognized as conrotatory.

See also

  • Symmetry rules!, Sophie Wilkinson Chemical & Engineering News January 27, 2003 Volume 81, Number 04 CENEAR 81 04 pp. 59 ISSN 0009-2347 Article
  • "SHMO calculator", Simple Huckel molecular orbital theory calculator Link

References

  1. ^ Stereochemistry of Electrocyclic Reactions R. B. Woodward, Roald Hoffmann J. Am. Chem. Soc.; 1965; 87(2); 395-397. doi:10.1021/ja01080a054
  2. ^ a b "On Molecular Orbital Correlation Diagrams, the Occurrence of Möbius Systems in Cyclization Reactions, and Factors Controlling Ground and Excited State Reactions. I," Zimmerman, H. E. J. Am. Chem. Soc., 1966, 88, 1564-1565
  3. ^ a b "On Molecular Orbital Correlation Diagrams, Möbius Systems, and Factors Controlling Ground and Excited State Reactions. II," Zimmerman, H. E. J. Am. Chem. Soc., 1966, 88, 1566-156.
  4. ^ "Biasing Reaction Pathways with Mechanical Force. Nature (2007) 446:423-427" (See also the corresponding "News and Views" in the same issue of Nature)
  5. ^ "Conservation of Orbital Symmetry Angew. Chem. Internat. Edit. (1969) 8:781-853" doi:10.1002/anie.196907811
  6. ^ Impossible Dreams E. J. Corey J. Org. Chem.; 2004; 69(9) pp 2917 - 2919; (Perspective) doi:10.1021/jo049925d
  7. ^ http://www.boston.com/news/globe/health_science/articles/2005/03/01/whose_idea_was_it/
  8. ^ A Claim on the Development of the Frontier Orbital Explanation of Electrocyclic Reactions Roald Hoffman; Angew. Chem. Int. Ed.; 2004; 43; 6586-6590. doi:10.1002/anie.200461440
  9. ^ Total Synthesis of Dihydrocostunolide E. J. Corey and Alfred G. Hortmann J. Am. Chem. Soc. 85 1963 pp 4033 - 4034; doi:10.1021/ja00907a030
  10. ^ The Total Synthesis of Dihydrocostunolide E. J. Corey, Alfred G. Hortmann J. Am. Chem. Soc.; 1965; 87(24); 5736-5742. doi:10.1021/ja00952a037
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