The Woodward–Hoffmann rules (or the pericyclic selection rules) are a set of rules devised by Robert Burns Woodward and Roald Hoffmann to rationalize or predict certain aspects of the stereochemistry and activation energy of pericyclic reactions, an important class of reactions in organic chemistry. The rules originate in certain symmetries of the molecule's orbital structure that any molecular Hamiltonian conserves. Consequently, any symmetry-violating reaction must couple extensively to the environment; this imposes an energy barrier on its occurrence, and such reactions are called symmetry-forbidden. Their opposites are symmetry-allowed.
Although the symmetry-imposed barrier is often formidable (up to c. 5 eV or 480 kJ/mol in the case of a forbidden [2+2] cycloaddition), the prohibition is not absolute, and symmetry-forbidden reactions can still take place if other factors (e.g. strain release) favor the reaction. Likewise, a symmetry-allowed reaction may be preempted by an insurmountable energetic barrier resulting from factors unrelated to orbital symmetry. All known cases only violate the rules superficially; instead, different parts of the mechanism become asynchronous, and each step conforms to the rules.
Background and terminology A pericyclic reaction is an organic reaction that proceeds via a single, concerted, cyclic transition state, the geometry of which allows for the continuous overlap of a cycle of (π and/or σ) orbitals.
The terms conrotatory and disrotatory describe the relative sense of bond rotation involved in electrocyclic ring-opening and -closing reactions. In a disrotatory process, the breaking or forming bond's two ends rotate in opposing directions (one clockwise, one counterclockwise); in a conrotatory process, they rotate in the same direction (both clockwise or both counterclockwise).
Eventually, it was recognized that thermally-promoted pericyclic reactions in general obey a single set of generalized selection rules, depending on the electron count and topology of the orbital interactions. The key concept of orbital topology or faciality was introduced to unify several classes of pericyclic reactions under a single conceptual framework. In short, a set of contiguous atoms and their associated orbitals that react as one unit in a pericyclic reaction is known as a component, and each component is said to be antarafacial or suprafacial depending on whether the orbital lobes that interact during the reaction are on the opposite or same side of the nodal plane, respectively. (The older terms conrotatory and disrotatory, which are applicable to electrocyclic ring opening and closing only, are subsumed by the terms antarafacial and suprafacial, respectively, under this more general classification system.)
History Woodward and Hoffmann developed the pericyclic selection rules as part of the broader community's effort to synthesize vitamin B12. Woodward wanted to know whether certain electrocyclic reactions might help, as such reactions exhibited striking stereospecificity, but could not predict which stereoisomer a reaction might select. In 1961, E. Havinga had noted that tachysterol underwent electrocyclic ring-closure in a conrotatory or disrotatory manner depending on (respectively) photochemical or thermal activation, and moreover that the stereospecificity could be explained through orbital symmetry, but it was unclear how far such a principle might extend. Hence, Woodward and Hoffman began extensive orbital-overlap calculations to analyze the behavior of open-chain conjugated polyenes.
Soon, Woodward and Hoffman realized that a simple set of rules governed the observed stereospecificity. In their 1965 publication, they summarized the experimental evidence and molecular orbital analysis as follows:
In an open-chain system containing 4n π electrons, the orbital symmetry of the highest occupied molecule orbital is such that a bonding interaction between the ends must involve overlap between orbital envelopes on opposite faces of the system and this can only be achieved in a conrotatory process. In open systems containing (4n + 2) π 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. In a photochemical reaction an electron in the HOMO of the reactant is promoted to an excited state leading to a reversal of terminal symmetry relationships and stereospecificity. In 1969, they would use correlation diagrams to state a generalized pericyclic selection rule equivalent to that now attached to their name: a pericyclic reaction is allowed if the sum of the number of suprafacial 4q + 2 components and number of antarafacial 4r components is odd. .
In the intervening four years, Howard Zimmerman and Michael J. S. Dewar proposed an equally general conceptual framework: the Möbius-Hückel concept, or aromatic transition state theory. In the Dewar-Zimmerman approach the orbital overlap topology (Hückel or Möbius) and electron count (4n + 2 or 4n) results in either an aromatic or antiaromatic transition state.
Meanwhile, Kenichi Fukui analyzed the frontier orbitals of such systems. A process in which the HOMO-LUMO interaction is constructive (results in a net bonding interaction) is favorable and considered symmetry-allowed, while a process in which the HOMO-LUMO interaction is non-constructive (results in bonding and antibonding interactions that cancel) is disfavorable and considered symmetry-forbidden.
Though conceptually distinct, aromatic transition state theory (Zimmerman and Dewar), frontier molecular orbital theory (Fukui), and orbital symmetry conservation (Woodward and Hoffmann) all make identical predictions. The Woodward–Hoffmann rules exemplify molecular orbital theory's power, and indeed helped demonstrate that useful chemical results could arise from orbital analysis. The discovery would earn Hoffmann and Fukui the 1981 Nobel Prize in Chemistry.The Nobel Prize in Chemistry 1981. Nobelprize.org. By that time, Woodward had died, and so was ineligible for the prize.
Priority dispute In a 2004 memoir, fellow Nobel Prize winner Elias James Corey attempted to claim that he originated Woodward and Hoffman's discoveries, and that Woodward neglected to credit him. In Corey's account, Corey visited Woodward's office around 8:30 p.m on Monday, May 4, 1964, before leaving for home. Woodward asked how to predict the type of ring a chain of atoms would form, and Corey suggested that the configuration of electrons could govern the course of the reaction. Woodward insisted the solution would not work, but Corey left drawings in the office, still confident in the suggestion. The next day, Woodward, excited, flew into Corey's office at lunchtime and presented Corey's idea as his own.Johnson, Carolyn Y. (March 1, 2005) Whose idea was it?. Boston Globe
Corey's claim is generally not credited. Hoffmann, Woodward's coworker, notes that Woodward presented "the crucial flash of enlightenment...in algebraic, rather than in pictorial or geometric form", which would be inconsistent with Corey's claims to a geometrical hint. Moreover, Corey relied on a stereospecific, electrocyclic reaction in a total synthesis published slightly before Woodward and Hoffmann's original publication:
If Corey had been thinking about the Woodward–Hoffmann rules around that time, he would have discussed the stereochemistry of the key electrocyclic reaction in his publication. Instead, Corey elided the matter.
Rule The Woodward–Hoffmann rules can be stated succinctly as a single sentence: A ground-state pericyclic process involving N electron pairs and A antarafacial components is symmetry-allowed if and only if N + A is odd. A ground-state pericyclic process is driven by surplus thermal energy (i.e., heat).
In the language of aromatic transition state theory, the Woodward–Hoffmann rules can be restated as follows: A pericyclic transition state involving (4n + 2) electrons with Hückel topology or 4n electrons with Möbius topology is aromatic and allowed, while a pericyclic transition state involving 4n-electrons with Hückel topology or (4n + 2)-electrons with Möbius topology is antiaromatic and forbidden. Often, the Woodward–Hoffmann rules are extended to analyze photochemical reactions, in which the surplus energy is provided by ultraviolet irradiation. If such processes occur purely in the excited state, then the Woodward–Hoffmann rules predict the exact reverse of the selection rule displayed above; that is: A pericyclic process involving N electron pairs and A antarafacial components is often favored under photochemical conditions if N + A is even. This can be rationalized by considering the correlation of the first electronic excited states of the reactants and products.
However, many formally pericyclic reactions taking place under photochemical irradiation exhibit complex mechanisms. Several modes of electronic excitation are usually possible, and electronically excited molecules may undergo intersystem crossing, radiationless decay, or relax to an unfavorable equilibrium geometry before the excited-state pericyclic process can take place. Thus, many apparent pericyclic reactions that take place under irradiation are actually thought to be stepwise processes involving diradical intermediates. Nevertheless, it is frequently observed that the pericyclic selection rules become reversed when switching from thermal to photochemical activation.
Pericyclic reactions involving an odd number of electrons are also known. With respect to application of the generalized pericyclic selection rule, these systems can generally be treated as though one more electron were involved.
Illustrative examples The interconversion of model cyclobutene and butadiene derivatives under thermal (heating) and photochemical (Ultraviolet irradiation) conditions is illustrative.
The Woodward–Hoffmann rules apply to either direction of a pericyclic process. Due to the inherent ring strain of cyclobutene derivatives, the thermodynamic equilibrium between the cyclobutene and the 1,3-butadiene strongly favors opening the ring. Irradiation causes reactions that can absorb photons to occur at a much faster rate and reactions that emit them occur more slowly, shifting the equilibrium to a photostationary state. Only the 1,3-butadiene absorbs significantly at higher wavelengths; hence, irradiation of the 1,3-butadiene at such a wavelength can result in high conversion to the cyclobutene.
Thermolysis of trans-1,2,3,4-tetramethyl-1-cyclobutene (1) afforded only one geometric isomer, (E,E)-3,4-dimethyl-2,4-hexadiene (2); the (Z,Z) and the (E,Z) geometric isomers were not detected in the product mixture. Similarly, thermolysis of cis-1,2,3,4-tetramethyl-1-cyclobutene (3) afforded only (E,Z) isomer 4. In both ring opening reactions, the carbons on the ends of the breaking σ-bond rotate in the same direction.Although the figure below shows both ends rotating clockwise, it is important to recognize that orbital symmetry only distinguishes between rotation in the same direction or opposing directions (conrotation vs. disrotation). The formation of the (Z,Z) isomer from ring opening of 1 (both ends rotating counterclockwise) is therefore also symmetry allowed. That the (Z,Z) isomer was not observed is likely due to unfavorable steric interactions between the inwardly rotating methyl groups. (In other cases, the preference for clockwise or counterclockwise bond rotation may be controlled by stereoelectronic factors: see torquoselectivity.)