HOMO-LUMO interactions 4 + 2 cycloadditions

When both the 1,3-dipoIe and the dipolarophile are unsymmetrical, there are two possible orientations for addition. Both steric and electronic factors play a role in determining the regioselectivity of the addition. The most generally satisfactory interpretation of the regiochemistry of dipolar cycloadditions is based on frontier orbital concepts. As with the Diels-Alder reaction, the most favorable orientation is that which involves complementary interaction between the frontier orbitals of the 1,3-dipole and the dipolarophile. Although most dipolar cycloadditions are of the type in which the LUMO of the dipolarophile interacts with the HOMO of the 1,3-dipole, there are a significant number of systems in which the relationship is reversed. There are also some in which the two possible HOMO-LUMO interactions are of comparable magnitude. 

Benzyne shares a feature with A in the [2+2] cycloaddition reactions. The HOMO-LUMO interaction prefers the three-centered interaction (Scheme 4) [115]. This is in agreement with the calculated reaction path [116]. 

Fig. 6.13. HOMO-LUMO interactions in the [2 + 2] cycloadditions of an alkene and a ketene (a) frontier orbitals of the alkene and ketene (b) [2tts + 2ttJ representation of suprafacial addition to the alkene and antarafacial addition to the ketene (c) [2tts + (2tts + 2tts)] alignment of orbitals.

Cycloaddition reactions using tropone or another cyclic triene as the 6ji partner have been abundantly described in the literature. It has been found that virtually all metal-free [6 + 4] cycloadditions of cyclic trienes afford predominantly exo adducts. This has been rationalized by consideration of the HOMO-LUMO interactions between the diene and triene partners. An unfavorable repulsive secondary orbital interaction between the remaining lobes of the diene HOMO and those of the triene LUMO develops during an endo approach. The exo transition state is devoid of this interaction (Figure 9). 

Fig. 6.2. HOMO-LUMO interactions rationalize regioselectivity of Diels-Alder cycloaddition reactions.

The 1,3-dipolar cycloaddition of organic azides with nitriles could give rise to two regioisomers. Since organic azides are Type II 1,3-dipoles on the Sustmann classification (approximately equal HOMO-LUMO gaps between the interacting frontier orbital pairs) the reactions could be dipole HOMO or LUMO controled and the regioselectivity should be determined by the orbital coefficients for the dominant HOMO-LUMO interaction. Such systems show U-shaped kinetic curves in their... 

Thus far, in the alkaloid series discussed, the nitrogen atom has always been part of the core of the alkaloid strucmre, rather than acting in a dipolarophilic manner in the cycloaddition of the carbonyl ylide. Recently, Padwa et al. (117) addressed this deficiency by conducting model studies to synthesize the core of ribasine, an alkaloid containing the indanobenzazepine skeleton with a bridging ether moiety (Scheme 4.57). Padwa found that indeed it was possible to use a C = N 7i-bond as the dipolarophile. In the first generation, a substimted benzylidene imine (219) was added after formation of the putative carbonyl ylide from diazoketone 218. The result was formation of both the endo and exo adduct with the endo adduct favored in an 8 1 ratio. This indicates that the endo transition state was shghtly favored as dictated by symmetry controlled HOMO—LUMO interactions. 

Many aspects of intramolecular nitrile oxide cycloadditions are similar to those of the intermolecular ones. Due to the proximity of the reacting groups, however, there are also several items that differ significantly. While HOMO-LUMO interactions and steric effects direct the intermolecular nitrile oxide cycloaddition to 1-alkenes to produce 5-substituted isoxazolines, the intramolecular cases often show a different behavior. With most of them, regioselectivity is determined by geometric constraints and cycloadditions occur in the exo mode to furnish the annulated bicycle (Scheme 6.42). 

An additional point of interest concerns the behaviour of homo and lumo orbitals of reactants in allowed reactions. Fukui (1970, 1975) has pointed out that the frontier-orbital gap actually narrows as the reaction proceeds. This has been confirmed computationally for the cycloaddition of ethylene and butadiene (Townshend et al., 1976), and contrasts with what one might expect based on a static homo-lumo interaction. Such an interaction causes the energy gap between resultant orbitals to widen, as indicated in Fig. 29. 

Such cycloadditions involve the addition of a 2tt- electron system (alkene) to a 4ir- electron system (ylide) and have been predicted to occur in a concerted manner according to the Woodward-Hoffmann rules. The two most important factors involved in the cycloaddition reactions are (i) the energy and symmetry of the reacting orbitals and (ii) the thermodynamic stability of the cycloadduct. The reactivity of 1,3-dipolar systems has been successfully accounted for in terms of HOMO-LUMO interactions using frontier MO theory (71TL2717). This approach has been extended to explain the 1,3 reactivities of the nonclassical A,B-diheteropentalenes <77HC(30)317). 

Recently, Huisgen and coworkers have reported on the first unequivocal example of a nonconcerted 1,3-dipolar cycloaddition.27 Sustmann s FMO model of concerted cycloadditions envisions two cases in which the stepwise mechanism might compete with the concerted one.21 Two similar HOMO-LUMO interaction energies correspond to a minimum of rate and a diradical mechanism is possible, especially if stabilizing substituents are present. A second case is when the HOMO (l,3-dipole)-LUMO (dipolarophile) is strongly dominant in the transition state. The higher the difference in rr-MO energies of reac-... 

One requirement for a successful HOMO-LUMO interaction is that the symmetry of the HOMO must match the symmetry of the LUMO (either both symmetric or both antisymmetric). If so, then the interaction is symmetry allowed and will lead to productive cycloaddition. If file symmetries do not match, then the HOMO-LUMO overlap is symmetry forbidden and cycloaddition will not proceed. Molecular orbitals can be classified by their phase symmetry with respect to a plane normal to the n system. The symmetry is related to the number of nodal planes which occur in each individual molecular orbital. For the olefin component, file it orbital (HOMO) is symmetric with respect to this plane and file it orbital... 

The essential features of the Diels-Alder reaction are a four-electron n system and a two-electron it system which interact by a HOMO-LUMO interaction. The Diels-Alder reaction uses a conjugated diene as the four-electron n system and a it bond between two elements as the two-electron component. However, other four-electron it systems could potentially interact widi olefins in a similar fashion to give cycloaddition products. For example, an allyl anion is a four-electron it system whose orbital diagram is shown below. The symmetry of the allyl anion nonbonding HOMO matches that of the olefin LUMO (as does the olefin HOMO and the allyl anion LUMO) thus effective overlap is possible and cycloaddition is allowed. The HOMO-LUMO energy gap determines the rate of reaction, which happens to be relatively slow in this case. 

The cyclic HOMO-LUMO interaction bears a striking resemblance to the transition state for 1,3-dipolar cycloadditions. 

Figure 15.2 (Section 15.2.1) showed the stereostructures of the transition states of the [4+2]-cycloadditions between ethene or acetylene, respectively, and butadiene. The HOMOs and LUMOs of all substrates involved are shown in Figure 15.4. Figures 15.8 and 15.9 depict the corresponding HOMO/LUMO pairs in the transition states of the respective [4+2]-cycloaddi-tions. Evaluation of Equation 15.2 reveals two new bonding HOMO/LUMO interactions of comparable size in both transition states. Therefore, the transition states of both cycloadditions benefit from a stabilization that is attenuated by a large energy difference between the frontier orbitals involved. That is why fairly drastic conditions are require for these specific processes.

As with the transition state of the [4+2]-addition of butadiene and ethene (Figure 15.8) both HOMO/LUMO interactions are stabilizing in the transition state of the [2+2]-addition of ketene to ethene (Figure 15.13). This explains why [2+2]-cycloadditions of ketenes to alkenes—and similarly to alkynes—can occur in one-step reactions while this is not so for the additions of alkenes to alkenes (Section 15.2.3). 

Why do the Diels-Alder reactions with both normal and inverse electron demand occur under relatively mild conditions And, in contrast, why can [4+2]-cycloadditions between ethene or acetylene, respectively, and butadiene be realized only under extremely harsh conditions (Figure 15.1) Equation 15.2 described the amount of transition state stabilization of [4+2]-cycloadditions as the result of HOMO/LUMO interactions between the 7T-MOs of the diene and the dienophile. Equation 15.3 is derived from Equation 15.2 and presents a simplified estimate of the magnitude of the stabilization. This equation features a sum of two simple terms, and it highlights the essence better than Equation 15.2. 

The one-step cycloadditions ethene + ethene — cyclobutane and ethene + acetylene —> cyclobutene are unknown (see Figure 12.1). One can understand why this is so by analyzing the frontier orbital interactions in the associated transition states (Figure 12.10). Both HOMO/LUMO interactions are nonbonding. This circumstance contributes to the fact that the respective transition states are energetically out of reach. 

Another way to look at this resuft comes from recognizing the special entropy problem involved in cycloaddition reactions. A very precise orientation of the two molecules is required for two bonds to be formed at once. These reactions have large negative entropies of activation (Chapter 41)—order must be created at the transition state as the two components align with one another. The through-space attractive HOMO/LUMO interaction between the two molecules can lead to an initial association that can be compared to a squishy sandwich with... 

Under thermal conditions, the TS of the [2 + 2] cycloaddition is made up of if/1 (the LUMO) of one component and i[io (the HOMO) of the other. Positive overlap between the orbitals at both termini of the 1t systems can be obtained only if one of the components reacts antarafacially. This orientation is very difficult to achieve geometrically, and hence [2 + 2] cycloadditions do not normally proceed under thermal conditions. However, under photochemical conditions, one of the components has an electron promoted from fo to //1. Now the HOMO-LUMO interaction is between ) / of the photoexcited component and i// of the unexcited component, and thus both components can be suprafacial in the TS. The [2 + 2] cycloaddition of most alkenes and carbonyl compounds do in fact proceed only upon irradiation with light. 

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