Woodward–Hoffmann rules

The key concept of orbital topology or faciality was introduced to unify several classes of pericyclic reactions under a single conceptual framework.

In 1965, Woodward–Hoffmann realized that a simple set of rules explained the observed stereospecificity at the ends of open-chain conjugated polyenes when heated or irradiated.

In their original publication,[2] they summarized the experimental evidence and molecular orbital analysis as follows: 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[3][4] and Michael J. S. Dewar[5][6] 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.

On the other hand, under irradiation by ultraviolet light, a photostationary state is reached, a composition which depends on both absorbance and quantum yield of the forward and reverse reactions at a particular wavelength.

[12] On the other hand, the opposite stereochemical course was followed under photochemical activation: When the related compound (E,E)-2,4-hexadiene (5) was exposed to light, cis-3,4-dimethyl-1-cyclobutene (6) was formed exclusively as a result of electrocyclic ring closure.

The Woodward-Hoffmann rules explain these results through orbital overlap:In the case of a photochemically driven electrocyclic ring-closure of buta-1,3-diene, electronic promotion causes

In contrast, an excited-state pericyclic process takes place if a reactant is promoted to an electronically excited state by activation with ultraviolet light (i.e., irradiating the system, symbolized by hν).

It is important to recognize, however, that the operative mechanism of a formally pericyclic reaction taking place under photochemical irradiation is generally not as simple or clearcut as this dichotomy suggests.

Thus, many apparent pericyclic reactions that take place under irradiation are actually thought to be stepwise processes involving diradical intermediates.

That is, the introduction of a simple substituent that formally disrupts a symmetry plane or axis (e.g., a methyl group) does not generally affect the assessment of whether a reaction is allowed or forbidden.

For this reason, the Woodward–Hoffmann, Fukui, and Dewar–Zimmerman analyses are equally broad in their applicability, though a certain approach may be easier or more intuitive to apply than another, depending on the reaction one wishes to analyze.

Thus a more correct statement is that as a ground state molecule explores the potential energy surface, it is more likely to achieve the activation barrier to undergo a conrotatory mechanism.

The geometrically most plausible [π2s + π2s] mode is forbidden under thermal conditions, while the [π2a + π2s], [π2s + π2a] approaches are allowed from the point of view of symmetry but are rare due to an unfavorable strain and steric profile.

Here, there is a high energetic barrier to a photo-induced Diels-Alder reaction under a suprafacial-suprafacial bond topology due to the avoided crossing shown below.

The full molecular orbital correlation diagram is constructed in by matching pairs of symmetric and asymmetric MOs of increasing total energy, as explained above.

Taking first the first possibility, in the ground state, if a polyene has 4n electrons, the outer p-orbitals of the HOMO that form the σ bond in the electrocyclized product are of opposite signs.

Using FMO analysis, [1,j]-sigmatropic rearrangements are allowed if the transition state has constructive overlap between the migrating group and the accepting p orbital of the HOMO.

The terms conrotatory and disrotatory are sufficient for describing the relative sense of bond rotation in electrocyclic ring closing or opening reactions, as illustrated on the right.

The pericyclic selection rule states: A pericyclic process involving 4n+2 or 4n electrons is thermally allowed if and only if the number of antarafacial components involved is even or odd, respectively.In this formulation, the electron count refers to the entire reacting system, rather than to individual components, as enumerated in Woodward and Hoffmann's original statement.

In addition, in some cases, e.g., the Cope rearrangement, the same (not necessarily strained) transition state geometry can be considered to contain two supra or two antara π components, depending on how one draws the connections between orbital lobes.

Thus, to restate the results of aromatic transition state theory in the language of Woodward and Hoffmann, a 4n-electron reaction is thermally allowed if and only if it has an odd number of antarafacial components (i.e., Möbius topology); a (4n + 2)-electron reaction is thermally allowed if and only if it has an even number of antarafacial components (i.e., Hückel topology).

Notice that although the concept of phase and orbitals are replaced simply by the notion of electron density, this function still takes both positive and negative values.

The Woodward–Hoffmann rules are reinterpreted using this formulation by matching favorable interactions between regions of electron density for which the dual descriptor has opposite signs.

For the case of a [4+2] cycloaddition, a simplified schematic of the reactants with the dual descriptor function colored (red=positive, blue=negative) is shown in the optimal supra/supra configuration to the left.

[32] Similarly, 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.

[33] In this paper, they use ultrasound irradiation to induce a mechanical stress on link-functionalized polymers attached syn or anti on the cyclobutene ring.

It has been stated that Elias James 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 rebuttal published in the Angewandte Chemie,[36] 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.