Cycloaddition reactions frontier orbital theory

How can we predict whether a given cycloaddition reaction will occur with suprafacial or with antarafacial geometry According to frontier orbital theory, a cycloaddition reaction takes place when a bonding interaction occurs between the HOMO of one reactant and the LUMO of the other. An intuitive explanation of this rule is to imagine that one reactant donates electrons to the other. As with elec-trocyclic reactions, it s the electrons in the HOMO of the first reactant that are least tightly held and most likely to be donated. But when the second reactant accepts those electrons, they must go into a vacant, unoccupied orbital—the LUMO. 

According to the calculations at high levels of theory, the [4+2] cycloaddition reactions of dienes with the singlet ( A oxygen follow stepwise pathways [37, 38], These results, which were unexpected from the Woodward-Hoffmann rule and the frontier orbital theory, suggest that the [4+2] cycloadditions of the singlet ( A oxygen could be the reactions in the pseudoexcitation band. 

We now turn to the gas-phase 1,3-dipolar cycloaddition of fulminic acid to ethyne. The concerted, almost synchronous nature of this reaction might create the impression that the electronic mechanism of this process should be very similar to that of the Diels-Alder reaction. Such an expectation is reinforced by frontier orbital theory, which treats both reactions in very much the same way (see Ref. 32). The only significant differences are related to the fact that the lowest unoccupied MO (LUMO) for a linear 1,3-dipole... 

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. 

According to the frontier orbital theory,525 electron-withdrawing substituents lower the energies of the lowest unoccupied molecular orbital (LUMO) of the di-enophile thereby decreasing the highets occupied molecular orbital (HOMO)-LUMO energy difference and the activation energy of the reaction. 1,3-Butadiene itself is sufficiently electron-rich to participate in cycloaddition. Other frequently used dienes are methyl-substituted butadienes, cyclopentadiene, 1,3-cyclohexa-diene, and 1,2-dimethylenecyclohexane. 

A secondary orbital interaction has been used to explain other puzzling features of selectivity, but, like frontier orbital theory itself, it has not stood the test of higher levels of theoretical investigation. Although still much cited, it does not appear to be the whole story, yet it remains the only simple explanation. It works for several other cycloadditions too, with the cyclopentadiene+tropone reaction favouring the extended transition structure 2.106 because the frontier orbitals have a repulsive interaction (wavy lines) between C-3, C-4, C-5 and C-6 on the tropone and C-2 and C-3 on the diene in the compressed transition structure 3.55. Similarly, the allyl anion+alkene interaction 3.56 is a model for a 1,3-dipolar cycloaddition, which has no secondary orbital interaction between the HOMO of the anion, with a node on C-2, and the LUMO of the dipolarophile, and only has a favourable interaction between the LUMO of the anion and the HOMO of the dipolarophile 3.57, which might explain the low level or absence of endo selectivity that dipolar cycloadditions show. 

Nevertheless, frontier orbital theory undoubtedly works, though it is not as universally successful as the W-H rules. The most important example of its success is probably the field of cycloadditions.103 The Diels-Alder reaction displays, to a marked degree,... 

Note. Several people have contributed to this field, but in the account that follows, their names have not always been placed in the section corresponding to the work they did. The version of each topic presented here is not always that of any one of them—nor is it proper to link their names with some of the over-simple arguments used. In roughly chronological order, the principal contributors are R. B. Woodward and R. Hoffmann,1 and K. Fukui,3 for the frontier orbital theory of the Woodward-Hoffmann rules, and W. C. Herndon,112 R. Sustmann,113 N. T. Anh,114> 115 K. N. Houk40,116,117 and N. D. Epiotis,118 for the various aspects of selectivity in cycloaddition reactions. 

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. 

The reactions of fulvenes (373) also provide examples where the longest conjugated system available is not always the one involved in cycloadditions, but this time frontier orbital theory is rather successful in accounting for the experimental observations. The orbital energies and coefficients are illustrated in Fig. 4-71, where it can be seen that there is a node through C-l and C-6 in the HOMO. The result is that when a relatively unsubstituted fulvene might react either as a n6 or as a n2 component with an electron-deficient (low-energy LUMO) diene or dipole, it should react as a n2 component because... 

This section on periselectivity has been disproportionately long. It is one of those subjects which frontier orbital theory has rationalised reasonably well, for all its inherent limitations. It is a fitting close to this section to reflect upon the bewildering variety of cycloadditions shown by dimethylfulvene, and to reflect upon how difficult it would be to explain the pattern of their reactions without frontier orbital theory. 

Some 1,3-dipoles, such as azides and diazoalkanes, are relatively stable, isolable compounds however, most are prepared in situ in the presence of the dipolarophile. Cycloaddition is thought to occur by a concerted process, because the stereochemistry E or Z) of the alkene dipolarophile is maintained trans or cis) in the cycloadduct (a stereospecihc aspect). Unlike many other pericycUc reactions, the regio- and stereoselectivities of 1,3-dipolar cycloaddition reactions, although often very good, can vary considerably both steric and electronic factors influence the selectivity and it is difficult to make predictions using frontier orbital theory. 

Reactions of simple fulvenes with dienophiles commonly take place at C(2) and C(5) and those with dienes at C(2) and C(3), i.e. the latter proceed by a [2 + 4] rather than a [6 + 4] cycloaddition. This, and other features of cycloaddition reactions involving fulvenes can be nicely explained in terms of frontier orbital theory [234,235]. In some reactions fulvenes may participate as 6ir rather than 27t components, for example with diazomethane ... 

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 exclusive orientation observed in this reaction is unusual and cannot be adequately accounted for on the basis of frontier orbital theory. A similar inconsistency was also found on irradiation of azirine 233. The orientation of the cycloaddition reaction of aldehyde 233 proceeds in an alternate regiochemical sense from that observed with related bimolecular nitrile ylide-aldehyde cycloadditions where one obtains only d-oxazolines 235. In... 

An interpretation based on frontier molecular orbital theory of the regiochemistry of Diels Alder and 1,3-dipolar cycloaddition reactions of the triazepine 3 is available.343 2,4,6-Trimethyl-benzonitrile oxide, for example, yields initially the adduct 6.344... 

According to frontier molecular orbital theory (FMO), the reactivity, regio-chemistry and stereochemistry of the Diels-Alder reaction are controlled by the suprafacial in phase interaction of the highest occupied molecular orbital (HOMO) of one component and the lowest unoccupied molecular orbital (LUMO) of the other. [17e, 41-43, 64] These orbitals are the closest in energy Scheme 1.14 illustrates the two dominant orbital interactions of a symmetry-allowed Diels-Alder cycloaddition. 

Ab initio Hartree-Fock and density functional theory (DFT) calculations were performed to study transition geometries in the intramolecular hetero-Diels-Alder cycloaddition reactions of azoalkenes 20 (LJ = CH2, NFI, O) (Equation 1). The order of the reactivities was predicted from frontier orbital energies. DFT calculations of the activation energies at the B3LYP level were in full agreement with the experimental results described in the literature <2001JST(535)165>. 

The Diels-Alder reaction (47t 2ir cycloaddition) is by far the best studied reaction of dienes from both theoretical and experimental viewpoints. Frontier molecular orbital theory predicts three types of Diels-Alder reaction. Structural effects on rate constants show the existence of two types of reaction ... 

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