Pericyclic reactions frontier orbital theory

Btamp/e Another example of frontier orbital theory uses the reaction of phenyl-butadiene with phenylethylene. This reaction is a [4 + 2] pericyclic addition to form a six-membered ring. It could proceed with the two phenyl rings close to each other (head to head) or further away from each other (head to tail). 

The actual rates of thermally-allowed pericyclic reactions vary vastly, and frontier-orbital theory (14, 15, 16) has proven to be the primary basis for quantitative understanding and correlation of the factors responsible. It is therefore of interest to find the dominant frontier orbital interactions for the group transfer reactions hypothesized to occur. 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

The SC descriptions of the electronic mechanisms of the three six-electron pericyclic gas-phase reactions discussed in this paper (namely, the Diels-Alder reaction between butadiene and ethene [11], the 1,3-dipolar cycloaddition offulminic acid to ethyne [12], and the disrotatory electrocyclic ring-opening of cyclohexadiene) take the theory much beyond the HMO and RHF levels employed in the formulation of the most popular MO-based treatments of pericyclic reactions, including the Woodward-Hoffmarm mles [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman model [4—6]. The SC wavefunction maintains near-CASSCF quality throughout the range of reaction coordinate studied for each reaction but, in contrast to its CASSCF counterpart, it is very much easier to interpret and to visualize directly. 

More recently, molecular orbital theory has provided a basis for explaining many other aspects of chemical reactivity besides the allowedness or otherwise of pericyclic reactions. The new work is based on the perturbation treatment of molecular orbital theory, introduced by Coulson and Longuet-Higgins,2 and is most familiar to organic chemists as the frontier orbital theory of Fukui.3 Earlier molecular orbital theories of reactivity concentrated on the product-like character of transition states the concept of localization energy in aromatic substitution is a well-known example. The perturbation theory concentrates instead on the other side of the reaction coordinate. It looks at how the interaction of the molecular orbitals of the starting materials influences the transition state. Both influences on the transition state are obviously important, and it is therefore important to know about both of them, not just the one, if we want a better understanding of transition states, and hence of chemical reactivity. 

The Woodward-Hoffmann rules1 for pericyclic reactions can be explained by frontier orbital theory, as Fukui3 has demonstrated. If you already know anything about frontier orbital theory, it is quite likely that you know it as one of the ways in which the Woodward-Hoffmann rules are accounted for. If this is the case, you should leave out the next 23 pages, and turn to page 109. 

Most pericyclic reactions, though of course not all, are little influenced by Coulombic forces for example, it is well known that the polarity of the solvent has little effect on the rate of Diels-Alder reactions. We can therefore expect that a major factor influencing reactivity will be the size of the frontier orbital interaction represented by the third term of equation 2-7, p. 27. This is why this chapter is much the largest in this book the most dramatic successes of frontier orbital theory have been the explanations it has given to an amazingly large number of observations in pericyclic chemistry. 

So far, cycloadditions have been our only examples of pericyclic reactions. There are several other classes of pericyclic reactions, of which the most notable are cheletropic reactions, sigmatropic rearrangements and electrocyclic reactions. In essence, frontier orbital theory treats each of them as a cycloaddition reaction. 

Nevertheless, frontier orbital theory, for all that it works, does not explain why the barrier to forbidden reactions is so high. Perturbation theory uses the sum of all filled-with-filled and filled-with-unfilled interactions (Chapter 3), with the frontier orbitals making only one contribution to this sum. Frontier orbital interactions cannot explain why, whenever it has been measured, the transition structure for the forbidden pathway is as much as 40 kJ mol 1 or more above that for the allowed pathway. Frontier orbital theory is much better at dealing with small differences in reactivity. We shall return later in this chapter to frontier orbital theory to explain the much weaker elements of selectivity, like the effect of substituents on the rates and regioselectivity, and the endo rule, but we must look for something better to explain why pericyclic reactions conform to the Woodward-Hoffmann rules with such dedication. 

The conservation of orbital symmetry theory states that in-phase orbitals overlap during the course of a pericyclic reaction. The conservation of orbital symmetry theory was based on the frontier orbital theory put forth by Kenichi Fukui in 1954. Although Fukui s theory was more than 10 years old, it had been overlooked because of its mathematical complexity and Fukui s failure to apply it to stereoselective reactions. 

Analysis of a reaction by frontier orbital theory has additional benefits, particularly for predicting reactivity and stereochemistry. Woodward and Hoffman pointed out "that electrocyclic reactions followed the stereochemistry dictated by the symmetry, or nodal properties of the HOMO of the polyene".This concept of orbital symmetry will be important for discussions of all pericyclic reactions. Of particular importance is the difference in energy between the HOMO one Ji system and the LUMO of a second Jt-system, because this will be used to predict reactivity in pericyclic reactions (see below). 

Pericyclic reactions are often treated using FRONTIER-ORBITAL theory or the WOOD-WARD-HOFFMANN RULES. 

The Diels-Alder reaction (for which Otto Diels and Kurt Alder were awarded together the Nobel Prize in 1950) involves the reaction of a conjugated diene with another group containing a pi bond (referred to as a dienophile since it loves reacting with dienes). In the presence of heat, a diene and a dienophile will combine to give a cyclohexene product. This concerted mechanism is an example of a pericyclic reaction called a [4 -i- 2] cycloaddition since it involves the interaction of a four-electron % system (the diene) with a two-electron 71 system (the dienophile). While many examples of the Diels-Alder reaction can be easily described as a reaction between a nucleophile and electrophile (the approach to be taken here), the mechanism and the regjo- and stereochemistry of the product is usually described by frontier orbital theory in which the HOMO of the diene and the LUMO of the dienophile are matched. 

The way the substituents affect the rate of the reaction can be rationalised with the aid of the Frontier Molecular Orbital (FMO) theory. This theory was developed during a study of the role of orbital symmetry in pericyclic reactions by Woodward and Hoffinann and, independently, by Fukui Later, Houk contributed significantly to the understanding of the reactivity and selectivity of these processes. ... 

The period 1930-1980s may be the golden age for the growth of qualitative theories and conceptual models. As is well known, the frontier molecular orbital theory [1-3], Woodward-Hoffmann rules [4, 5], and the resonance theory [6] have equipped chemists well for rationalizing and predicting pericyclic reaction mechanisms or molecular properties with fundamental concepts such as orbital symmetry and hybridization. Remarkable advances in aeative synthesis and fine characterization during recent years appeal for new conceptual models. 

Houk, K.N. "Application of Frontier Molecular Orbital Theory to Pericyclic Reactions", in "Pericyclic Reactions", A.P. 

Frontier molecular orbital (FMO) theory 62) has provided new insights into chemical reactivity. This, and the simplicity of its application, has led to its widespread use, particularly in the treatment of pericyclic reactions 63). An FMO treatment depends on the energy of the highest occupied (HOMO) and lowest unoccupied molecular... 

The structural requirements of the mesomeric betaines described in Section III endow these molecules with reactive -electron systems whose orbital symmetries are suitable for participation in a variety of pericyclic reactions. In particular, many betaines undergo 1,3-dipolar cycloaddition reactions giving stable adducts. Since these reactions are moderately exothermic, the transition state can be expected to occur early in the reaction and the magnitude of the frontier orbital interactions, as 1,3-dipole and 1,3-dipolarophile approach, can be expected to influence the energy of the transition state—and therefore the reaction rate and the structure of the product. This is the essence of frontier molecular orbital (EMO) theory, several accounts of which have been published. 16.317 application of the FMO method to the pericyclic reactions of mesomeric betaines has met with considerable success. The following section describes how the reactivity, electroselectivity, and regioselectivity of these molecules have been rationalized. 

Three levels of explanation have been advanced to account for the patterns of reactivity encompassed by the Woodward-Hoffmann rules. The first draws attention to the frequency with which pericyclic reactions have a transition structure with (An + 2) electrons in a cyclic conjugated system, which can be seen as being aromatic. The second makes the point that the interaction of the appropriate frontier orbitals matches the observed stereochemistry. The third is to use orbital and state correlation diagrams in a compellingly satisfying treatment for those cases with identifiable elements of symmetry. Molecular orbital theory is the basis for all these related explanations. 

Although Otto Diels and Kurt Alder won the 1950 Nobel Prize in Chemistry for the Diels-Alder reaction, almost 20 years later R. Hoffmann and R. B. Woodward gave the explanation of this reaction. They published a classical textbook, The Conservation of Orbital Symmetry. K. Fukui (the co-recipient with R. Hoffmann of the 1981 Nobel Prize in Chemistry) gave the Frontier molecular orbital (FMO) theory, which also explains pericyclic reactions. Both theories allow us to predict the conditions under which a pericyclic reaction will occur and what the stereochemical outcome will be. Between these two fundamental approaches to pericyclic reactions, the FMO approach is simpler because it is based on a pictorial approach. Another method similar to the FMO approach of analyzing pericyclic reactions is the transition state aromaticity approach. 

The comparison of the energies of a-, a -, 77- and 77 -orbitals of ethene is shown in Fig. 8.6. The bonding electrons are placed in the two orbitals with lowest energies, ct and 77, in the ground state of ethene. The 77-orbital is the highest occupied molecular orbital (HOMO) and 77 -orbital is the lowest unoccupied molecular orbital (LUMO). Both HOMO and LUMO are referred to as frontier orbitals (see FMO theory ) and are used in analyzing pericyclic reactions. 

Two studies on the mechanism of this type of [4 + 2] cycloaddition which have led to very di erent interpretations have appeared. Mock and Nugent suggested that the Diels-Alder reactions of N-sulfi-nyl-p-toluenesulfonamide are stepwise, ionic processes. On the other hand, Hanson and Stockbum prefer a concerted, pericyclic mechanism in accord with frontier molecular orbital theory. Both proposals satisfactorily rationalize the observed regioselectivity of these reactions. 

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