Woodward-Hoffmann rules

The Woodward - Hoffmann rules explain which products will be obtained in the course of certain concerted organic reactions. In particular, they are applicable for pericyclic reactions, in which the reaction consists of a reorganization of pairs of electrons. The rules were set up around 1965 by Woodward and Hoffmann Originally, the rules were used as guideline in the total synthesis of the vitamin B 2. 

Precursors of these rules are the Wigner - Wittmer rules [23], concerning the symmetry of chemical reactions. The Wigner- Wittmer rules deal with the conservation of spin and orbital angular momentum in the course of the reaction of diatomic molecules. 

The Woodward-Hoffmann (W-H) rules are qualitative statements regarding relative activation energies for two possible modes of reaction, which may have different stereochemical outcomes. For simple systems, the rules may be derived from a conservation of orbital symmetry, but they may also be generalized by an FMO treatment with conservation of bonding. Let us illustrate the Woodward-Hoffmann rules with a couple of examples, the preference of the 4 + 2 over the 2 + 2 product for the reaction of butadiene with ethylene, and the ring-closure of butadiene to cyclobutene. 

A face-to-face reaction of two jr-orbitals to form a cyclobutane involves the formation of two new C—C a-bonds. The reaction may be imagined to occur under the preservation of symmetry, in this case C2v, i.e. concerted (one-step, no intermediates) and synchronous (both bonds are formed at the same rate). 

It is clearly seen that the HOMO-LUMO interaction leads to the formation of one bonding and one antibonding orbital, i.e. this is not a favourable interaction. The FMO approach also suggests that the 2 + 2 reaction may be possible if it could occur with bond formation on opposite sides (Antarafacial) for one of the fragments. 

Although the 2s + 2a reaction is Woodward-Hoffmann allowed, it is sterically so hindered that thermal 2 + 2 reactions in general are not observed. Photochemical 2 + 2 reactions, however, are well known.  

The 4s + 2s reaction of a diene with a double bond can in a concerted and synchronous reaction be envisioned to occur with the preservation of C, symmetry. 

The crucial moment in the formulation of the systematic theory of pericyclic reactions is undoubtedly represented by the advent of the so-called Woodward-Hoffmaim rules [20-22], on the basis of which it was possible to explain and to rationalize the remarkable stereospecificily of these reactions. This specificity manifests itself in the predominant formation of only one stereoisomer as well as by the dramatic change of the preferred reaction mechanism depending on whether the reaction proceeds under the conditions of thermal or photochemical initiation. Thus, e.g., the thermal cyclization of butadiene to cyclobutene proceeds by the conrotatory mechanism, while for the photochemical reaction the disrotatory reaction is prefened. 

Similarly for 2 + 2 cycloadditions the 2g + 2g mechanism is preferred for thermal reaction, whereas the alternative 2g + 2g mechanism dominates under the conditions of the photochemical reaction. The reaction mechanism which is preferred for a given type of reaction and reaction conditions (thermal vs. photochemical initiation) by the Woodward-Hoffinann rules is called symmetry-allowed, whereas the remaining alternative process is synunetiy-forbidden. 

The complete survey of the predictions of the Woodward-Hof nann rules is summarized in Table 1 from which it follows that the decisive role in the classification of the reaction mechanism is played by the size of the system quantitatively characterized by the number of electrons (4n, 4n+2) actively participating in the process. 

The original intuitive formulation of Woodward-Hof nann rules related the stereospecificity of pericyclic reactions to the differences in the symmetry of the highest occupied orbital (HOMO). Thus, e.g., the dominance of comotatory and disrotatory reaction for the cyclization of 1,3 butadiene and 1,3,5 hexatriene respectively is, from this point of view, easily predicted from the simple scheme visualizing the creation of the single bond in the cyclic product by the overlap of the terminal p orbitals of the linear skeleton. 

Few theories of stereospecificity have touched the analytic sensitivities and moved the creative abilities of chemists as that contained in the classic papers of Woodward and Hoffmann in 1965. Their initial ideas had developed into a cogent set of Rules described in a later publication, which will be summarized below. 

The Rules for the stereospecificity apply only to pericyclic reactions which are concerted. The Rules apply neither to non-concerted reactions nor to those that are not pericyclic. Pericyclic reactions are those which involve a monocyclic transition state having a conjugated array of interacting orbitals, one per atom. Three types of pericyclic processes have been recognized electrocyclic reactions, cycloadditions, and sigmatropic shifts. 

The course of this reaction is conrotatory, i.e. the p orbitals at the termini of the polyene rotate in the same direction to make (or break) the a bond in a concerted reaction, if 4n electrons are involved. If 4/2 + 2 electrons are involved, the concerted reaction occurs in a disrotatory manner, i.e. the p orbitals at the termini rotate in opposite directions. 

A generalization allows easy application of the Rules to any concerted pericyclic reaction involving two-electron bonds for the allowed reaction there must always be an odd number of suprafacial (as opposed to antarafacial) uses of bonds. Here, suprafacial is defined as utilizing both atoms of a C7 bond with retention of configuration or both with inversion with a Trbond, the p orbitals must be used from the same face of the bond. An antarafacial use of a cr bond would give retention at one atom and inversion at the other with a tt bond, the p orbitals must be used from opposite faces of the bond. 

The generalized Rules might seem arbitrary, but they are based on fundamental considerations of cyclic delocalization in transition states. If there are 4 + 2 electrons involved, the number of negative overlaps in basis set orbitals must be even for the delocalization to occur, i.e. stabilization of the transition state. If there are 4n electrons involved, the number of negative overlaps in basis set orbitals must be odd for delocalization to occur. The former is a so-called Hiickel tt overlap system while the latter is a Mobius tt overlap system. 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

The Woodward-Hoffifumn (WH) rules are qualitative statements regarding relative activation energies for two possible modes of reaction, which may have different stereochemical outcomes. For simple systems the rules may be derived from a 

The ring closure of a diene to a cyclobutene can occur with rotation of the two termini in the same conrotatory) or opposite disrotatory) directions. For suitable substituted compounds, these two reaction modes lead to products with different stereochemistry. 

The Woodward-Hoffmann allowed reactions can be classified according to how many electrons are involved, and whether the reaction occurs thermally or photochemically, as shown in Table 15.1. 

The state correlation diagrams give an indication of the minimum theoretical level necessary for describing a reaction. For allowed reactions, the reactant configuration 

The overlap between the nearest carbon p-orbital and 4 2 is the largest contribution. 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in 

The Woodward-Hoffmann (WH) rules are qualitative statements regarding relative 

While the orbital and state diagrams can only be rigorously justified in the simple parent system, where symmetry is present, the addition of substituents normally only alters the shape of the relevant orbitals slightly. The nodal stmcture of the orbitals is preserved for a large range of substituted systetns, and the preservation of bonding  

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Electi ocyclic reactions are examples of cases where ic-electiDn bonds transform to sigma ones [32,49,55]. A prototype is the cyclization of butadiene to cyclobutene (Fig. 8, lower panel). In this four electron system, phase inversion occurs if no new nodes are fomred along the reaction coordinate. Therefore, when the ring closure is disrotatory, the system is Hiickel type, and the reaction a phase-inverting one. If, however, the motion is conrotatory, a new node is formed along the reaction coordinate just as in the HCl + H system. The reaction is now Mdbius type, and phase preserving. This result, which is in line with the Woodward-Hoffmann rules and with Zimmerman s Mdbius-Huckel model [20], was obtained without consideration of nuclear symmetry. This conclusion was previously reached by Goddard [22,39]. 

We have seen (Section I) that there are two types of loops that are phase inverting upon completing a round hip an i one and an ip one. A schematic representation of these loops is shown in Figure 10. The other two options, p and i p loops do not contain a conical intersection. Let us assume that A is the reactant, B the desired product, and C the third anchor. In an ip loop, any one of the three reaction may be the phase-inverting one, including the B C one. Thus, the A B reaction may be phase preserving, and still B may be attainable by a photochemical reaction. This is in apparent contradiction with predictions based on the Woodward-Hoffmann rules (see Section Vni). The different options are summarized in Figure 11. 

Along "Reaction Paths", Orbitals Can be Connected One-to-One According to Their Symmetries and Energies. This is the Origin of the Woodward-Hoffmann Rules I. Reduction in Symmetry... 

Along "reactionpaths", configurations can be connected one-to-one according to their symmetries and energies. This is another part of the Woodward-Hoffmann rules... 

The direct connection of rings A and D at C l cannot be achieved by enamine or sul> fide couplings. This reaction has been carried out in almost quantitative yield by electrocyclic reactions of A/D Secocorrinoid metal complexes and constitutes a magnificent application of the Woodward-Hoffmann rules. First an antarafacial hydrogen shift from C-19 to C-1 is induced by light (sigmatropic 18-electron rearrangement), and second, a conrotatory thermally allowed cyclization of the mesoionic 16 rc-electron intermediate occurs. Only the A -trans-isomer is formed (A. Eschenmoser, 1974 A. Pfaltz, 1977). 

Frontier orbital analysis is a powerful theory that aids our understanding of a great number of organic reactions Its early development is attributed to Professor Kenichi Fukui of Kyoto University Japan The application of frontier orbital methods to Diels-Alder reactions represents one part of what organic chemists refer to as the Woodward-Hoffmann rules a beautifully simple analysis of organic reactions by Professor R B Woodward of Harvard University and Professor Roald Hoffmann of Cornell University Professors Fukui and Hoffmann were corecipients of the 1981 Nobel Prize m chemistry for their work... 

The importance of orbital overlap in determining why certain chemical reactions proceed easily while other similar reactions do not go at all was first advanced by Woodward and Hoffmann, and collectively their ideas are now known as the Woodward-Hoffmann rules. Applications of these ideas can be found in Chapter 21. 

UV irradiation. Indeed, thermal reaction of 1-phenyl-3,4-dimethylphosphole with (C5HloNH)Mo(CO)4 leads to 155 (M = Mo) and not to 154 (M = Mo, R = Ph). Complex 155 (M = Mo) converts into 154 (M = Mo, R = Ph) under UV irradiation. This route was confirmed by a photochemical reaction between 3,4-dimethyl-l-phenylphosphole and Mo(CO)6 when both 146 (M = Mo, R = Ph, R = R = H, R = R" = Me) and 155 (M = Mo) resulted (89IC4536). In excess phosphole, the product was 156. A similar chromium complex is known [82JCS(CC)667]. Complex 146 (M = Mo, R = Ph, r2 = R = H, R = R = Me) enters [4 -H 2] Diels-Alder cycloaddition with diphenylvinylphosphine to give 157. However, from the viewpoint of Woodward-Hoffmann rules and on the basis of the study of UV irradiation of 1,2,5-trimethylphosphole, it is highly probable that [2 - - 2] dimers are the initial products of dimerization, and [4 - - 2] dimers are the final results of thermally allowed intramolecular rearrangement of [2 - - 2] dimers. This hypothesis was confirmed by the data obtained from the reaction of 1-phenylphosphole with molybdenum hexacarbonyl under UV irradiation the head-to-tail structure of the complex 158. 

Roald Hoffmann (1937—) was born in Zloczow, Poland, just prior to World War II. As a boy, he survived the Holocaust by hiding in the attic of a village schoolhouse. In 1949, he immigrated to the United States, where he received an undergraduate degree at Columbia University and a Ph.D. at Harvard University in 1962. During a further 3-year stay at Harvard as Junior Fellow, he began the collaboration with R. B. Woodward that led to the development of the Woodward-Hoffmann rules for pericyclic reactions. In 1965, he moved to Cornell University, where he remains as professor. He received the 1981 Nobel Prize in chemistry. 

The Woodward-Hoffmann rules for pericyclic reactions require an analysis of all reactant and product molecular orbitals, but Kenichi Fukui at Kyoto Imperial University in Japan introduced a simplified version. According to Fukui, we need to consider only two molecular orbitals, called the frontier orbitals. These frontier orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In ground-state 1,3,5-hexa-triene, for example, 1//3 is the HOMO and excited-stale 1,3,5-hexatriene, however, 5 is the LUMO. 

Scheme 2. Thermally allowed 8 n electron and 6 k electron electro-cyclizations (Woodward-Hoffmann rules).

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