The Generalized Orbital Symmetry Rule

The field of pericyclic chemistry has spawned a large amount of terminology. We ve already introduced pericyclic , concerted , stepwise , allowed , and forbidden . We need to introduce a few more terms here to further facilitate our analysis of pericyclic reactions, and then give a rule that can be used to analyze all pericyclic reactions. 

Definitions of suprafacial and antarafacial for various types of orbitals. 

With these descriptors in hand, we can look at the generalized orbital symmetry rule. There is a definite binary nature to the theory of pericyclic reactions. For cycloadditions, [2-f2] is forbidden (all suprafacial), whereas [4-F2] is allowed (all suprafacial). Continuing with the series, [6+2] is forbidden, and [8+2] is allowed. We will also encounter patterns in the other kinds of pericyclic reactions presented electrocyclic reactions, sigmatropic shifts, etc. Based on patterns such as these. Woodward and Hoffmann proposed the following rule for all pericyclic reactions  

A periei/clic reaction is allowed if the number of4q + 2 suprafacial plus 4r antarafacial 

Here q and r are integers. This means that any 2-, 6-, 10-, 14-electron, etc., suprafacial component is considered, and any 0-, 4-, 8-, 12-electron, etc., antarafacial component is considered when determining if there are an odd number of components for the reaction under consideration. If the number is even, the reaction is forbidden. 

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This is a very powerful rule, and it is especially useful when there are several components to a pericyclic reaction. With several components it is often difficult to identify the appropriate HOMOs and LUMOs for an FMO analysis, and difficult to quickly write an orbital or state correlation diagram. In such cases, aromatic transition state theory, or the generalized orbital symmetry rule, are the easiest approaches for analyzing the reaction. It is your decision as to which works best for you. 

The FMO analysis is as shown in Figure 15.10 C. The HOMO-LUMO interaction is now favorable and leads naturally to the formation of the two new bonds. Figure 15.10 D shows the aromatic transition state analysis. Using the looped lines, we have designated the full cyclic array of interactions. As shown, there is one node in the system, so this is a Mobius system. Since there are four electrons in the cyclic array, the reaction is allowed. By the generalized orbital symmetry rule, this approach trajectory ([ 2s + is thermally allowed [only the component fits the 4q + 2)s and (4r)a formulas]. In summary, it is incorrect to say that... 

Analysis of electrocyclic reactions using a variety of methods and the various conclusions that are drawn. A. FMO theory for ring-opening. The LUMOs of the ir systems are compared to the HOMO of the C-C o bond in cyclobutene and 1,3-cyclohexadiene. B. The Hiickel/Mobius approach. C. Using the generalized orbital symmetry rule. Note, as always, that all the methods predict the same outcome. 

The analysis of the generalized orbital symmetry rule nicely follows from the above discussion (Figure 15.17 C). The conrotatory opening of cyclobutene is a -I- 2a] reaction and therefore allowed, while the disrotatory reaction is [tt2s -H 2J and forbidden. The conrotatory opening of 1,3-cyclohexadiene is a [ 4s + path that is forbidden, while the disrotatory + selection rules listed in Table 15.2. 

Lastly, we can examine all these different shifts using the generalized orbital symmetry rule. Various examples of allowed combinations are shown in Figure 15.21 D. The [3,3] shift is best viewed as a three-component reaction, where all three act in a suprafacial manner in order to be allowed. Generalizing all these approaches for two-component reactions yields Table 15.3, which summarizes sigmatropic shifts. 

Theoretical approaches to chelotropic reactions, showing only allowed reaction paths. A. An FMO analysis. B. Hiickel vs. Mobius transition states. C. Use of the generalized orbital symmetry rule. 

Occasionally, though, you will run across a more exotic pericyclic process, and will want to decide if it is allowed. In a complex case, a reaction that is not a simple electrocyclic ringopening or cycloaddition, often the basic orbital symmetry rules or FMO analyses are not easily applied. In contrast, aromatic transition state theory and the generalized orbital symmetry rule are easy to apply to any reaction. With aromatic transition state theory, we simply draw the cyclic array of orbitals, establish whether we have a Mobius or Hiickel topology, and then count electrons. Also, the generalized orbital symmetry rule is easy to apply. We simply break the reaction into two or more components and analyze the number of electrons and the ability of the components to react in a suprafacial or antarafacial manner. 

Examine the following complex pericyclic reactions, and designate them using the electron count and suprafacial / antarafacial terminology. State if they are allowed or forbidden ba.sed upon the generalized orbital symmetry rule. 

The generalized orbital symmetry selection rules are given below. The bases of these rules are discussed for each of the major classes of sigmatropic rearrangements. 

The calculations thus fail to indicate any substantial energy preference for the allowed paths with respect to the forbidden ones. An inspection of the overall shape of the surface confirms, however, that along the allowed CCW path a less steep slope has to be climbed (Fig. 18). The general conclusion is that steric and symmetry factors are so intimately interwoven that it is impossible to distinguish their relative importance in cases where the magnitudes of the two effects are similar. This can perhaps be taken as a warning that orbital symmetry rules should only be applied with some caution to very strained systems. 

According to the generalized Woodward-Hoffmann rule, the total number of (4q + 2)s and (4r)0 components must be odd for an orbitally allowed process. Thus, Eq. (14) is an allowed, and Eq. (13) a forbidden sigmatropic rearrangement. The different fluxional characteristics of tetrahapto cyclooctatetraene (52, 138) and substituted benzene (36, 43, 125) metal complexes may therefore be related to orbital symmetry effects. 

We have emphasized that the Diels-Alder reaction generally takes place rapidly and conveniently. In sharp contrast, the apparently similar dimerization of olefins to cyclobutanes (5-49) gives very poor results in most cases, except when photochemically induced. Fukui, Woodward, and Hoffmann have shown that these contrasting results can be explained by the principle of conservation of orbital symmetry,895 which predicts that certain reactions are allowed and others forbidden. The orbital-symmetry rules (also called the Woodward-Hoffmann rules) apply only to concerted reactions, e.g., mechanism a, and are based on the principle that reactions take place in such a way as to maintain maximum bonding throughout the course of the reaction. There are several ways of applying the orbital-symmetry principle to cycloaddition reactions, three of which are used more frequently than others.896 Of these three we will discuss two the frontier-orbital method and the Mobius-Huckel method. The third, called the correlation diagram method,897 is less convenient to apply than the other two. 

The aim of the present review is to provide chemists with a general survey of the different techniques now available for the theoretical evaluation of reaction paths. Qualitative work is based nowadays mainly on orbital symmetry rules this topic is given special emphasis here, since the method is of general use in everyday chemistry. Methods that require actual computation are described in the second part of this review under the heading semi-quantitative methods, since a complete, non-approximate, quantum-mechanical calculation of a reaction rate has never yet been carried out, even for the simplest systems. 

A great deal of effort has been expended to model the transition structures of concerted pericyclic reactions. All of the major theoretical approaches, semiempirical MO, ab initio MO, and DFT have been applied to the problem and some comparisons have been made. The conclusions drawn generally parallel the orbital symmetry rules in their prediction of reactivity and stereochemistry and provide additional insight into substituent effects. 

We have now considered three viewpoints from which thermal electrocyclic processes can be analyzed symmetry characteristics of the frontier orbitals, orbital correlation diagrams, and transition-state aromaticity. All arrive at the same conclusions about stereochemistry of electrocyclic reactions. Reactions involving 4n + 2 electrons will be disrotatory and involve a Huckel-type transition state, whereas those involving 4n electrons will be conrotatory and the orbital array will be of the Mobius type. These general principles serve to explain and correlate many specific experimental observations made both before and after the orbital symmetry rules were formulated. We will discuss a few representative examples in the following paragraphs. 

Two reviews deal with the relation between homogeneous and heterogeneous catalysis. One of these reviews is of a general physical and theoretical nature, while the other is concerned with specific classes of compounds — alkenes, alkynes, and fats — and concentrates on their hydrogenation and isomerization. Homogeneous catalysis by ruthenium complexes has been reviewed. The application of molecular orbital symmetry rules, to organic as well as to organometallic reaction mechanisms, has been discussed, and a set of rules similar to, but simpler to apply than, the Woodward-Hoffmann rules has been described. ... 

Although in principle the thermal [2-I-2-I-2] cycloaddition process is allowed by orbital symmetry rules, there are problems with the entropy component, which may be overcome by using transition metal catalysis. This approach (Scheme 2.35) is one of the most convenient for the synthesis of pyridines 2.100. Metal-induced cycloaddition of two alkyne and one nitrile molecules has been described in general reviews of cycloaddition reactions [3,4]. However in some reviews on heterocycles the nitriles are considered as equivalent to alkyne in the [2+2+2] cyclotrimerization reaction [76], in particular, for the synthesis of pyridines and pyridinones in the reactions catalyzed by cobalt, ruthenium, titanium, and zirconium. 

More general orbital symmetry requirements might be expected to affect the probability of entering an excited state. A good example [45] is that of the formation of excited SO2 and NO2 discussed below. The relative ease with which the kinetic parameters may be obtained for such simple reactions allows quantitative confirmation of the importance of this effect. The other reaction for which such factors have been discussed is that of the dioxetans. It is more difficult to produce convincing evidence of the operation of symmetry rules in this case, although many calculations have been performed in pursuit of the idea [37-41]. A more complete discussion appears in the section dealing with the dioxetans (Chap. V). 

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