Transition state HOMO-LUMO interactions

The detailed study of the molecular orbitals in the different species allowed a better understanding of the interactions under way. It was proved that the charge-transfer from the HOMO of the metal moiety to the n orbital of C02 is the most important interaction in the transition state and that the anti-bonding mixing of the n orbital of C02 also plays a significant role. The leading role of this HOMO-LUMO interaction also explains why the M-OCOH species is more easily formed than the M-COOH species. 

The endo selectivity in many Diels-Alder reactions has been attributed to attractive secondary orbital interactions. In addition to the primary stabilizing HOMO-LUMO interactions, additional stabilizing interactions between the remaining parts of the diene and the dienophile are possible in the endo transition state (Figure 3). This secondary orbital interaction was originally proposed for substituents having jr orbitals, e.g. CN and CHO, but was later extended to substituents with tt(CH2) type of orbitals, as encountered in cyclopropene57. 

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). 

The features in Figure 15.2 are believed to be due to electron transitions from the highest occupied molecular orbital states to lowest unoccupied molecular orbital states (HOMO-LUMO). Specifically, for single molecules and dilute solutions, the absorption in the blue part of the spectrum is proposed to be caused by the aromatic structure of TNT [4], probably involving it to it transitions.1 In the solid state, where the molecules are stacked up on top of each other, interactions between the molecules occur causing the energy levels to split into higher... 

Cycloadditions of ketenes and alkenes have been shown to have synthetic utility for the preparation of cyclobutanones.101 The stereoselectivity of ketene-alkene cycloaddition can be analyzed in terms of the Woodward-Hoffmann rules.102 To be an allowed process, the [2n + 2n] cycloaddition must be suprafacial in one component and antarafacial in the other. An alternative description of the transition state is a [2ns + (2ns + 2ns)] addition.103 Figure 6.6 illustrates these transition states. The ketene, utilizing its low-lying LUMO, is the antarafacial component and interacts with the HOMO of the alkene. The stereoselectivity of ketene cycloadditions can be rationalized in terms of steric effects in this transition state. Minimization of interaction between the substituents R and R leads to a cyclobutanone in which these substituents are cis. This is the... 

Fig. 6.6. HOMO-LUMO interactions in the [2 + 2] cycloaddition of an alkene and a ketene. (a) Frontier orbitals of alkene and ketene. (b) [2ks + 2na Transition state required for suprafacial addition to alkene and antarafacial addition to ketene, leading to R and R in cis orientation in cyclobutanone products, (c) [2ns + (2ns + 271,)] alternative transition state.

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. 

We may redraw 6 as 7a and 7b, in terms of frontier MOs. Here we emphasize the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) interactions that operate in the transition state 7a depicts the LUMO(carbene)/HOMO(alkene) or p-n interaction 7b shows the HOMO (carbene)/LUMO(alkene) or a-71 interaction. These formulations are especially... 

Figure 10.15 Backside attack by a nucleophile. Now HOMO-LUMO interaction is possible, and the transition state is stabilized. (As in the H- + F2 process, Figure 10.13, there will also be a smaller HOMO-HOMO interaction here. Because it is a filled-filled interaction, it will not alter the energy.)...

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-... 

Despite mechanistic complications, however, it appears very likely that most, if not all, of the facile and synthetically attractive carbometallation reactions involve, at a critical moment, concerted addition of carbon-metal bonds where the synergistic HOMO-LUMO interactions shown in Scheme 4.3, akin to those for the concerted hydrometallation reactions, provide a plausible common mechanism. This mechanism requires the ready availability of a metal empty orbital. It also requires that addition of carbon-metal bonds be strictly syn, as has generally been observed. Perhaps more important in the present discussion is that concerted syn carbometallation must proceed via a transition state in which a carbon-metal bond and a carbon-carbon bond become coplanar. Under such constraints, one can readily see how chirally discriminated carbon-metal bonds can select either re or si face of alkenes. In principle, the mechanistic and stereochemical considerations presented above are essentially the same as for related concerted syn hydrometalla-tion. In reality, however, carbometallation is generally less facile than the corresponding hydrometallation, which may be largely attributable to more demanding steric and... 

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.

HOMO/LUMO interactions are nonbonding. This circumstance contributes to the fact that the respective transition states are energetically out of reach. 

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). 

In contrast to the [4+2]-additions of butadiene to ethene or acetylene (Figures 15.8 and 15.9), the two HOMO/LUMO interactions stabilize the transition state of the [2+2]- addition of ketenes to alkenes to a very different extent. Equation 15.2 reveals that the larger part of the stabilization is due to the LUMOketene/HOMOethene interaction. This circumstance greatly affects the geometry of the transition state. If there were only this one frontier orbital interaction in the transition state, the carbonyl carbon of the ketene would occupy a position in the transition state that would be perpendicular above the midpoint of the ethene double bond. The Newman projection of the transition state (Figure 15.11) shows that this is almost the case but... 

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. 

In contrast to the [4+2]-additions of butadiene to ethene or acetylene (Figures 12.8 and 12.9), the two HOMO/LUMO interactions stabilize the transition state of the [2+2]-... 

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... 

An additional feature revealed by the considerations about molecular distortions is that as the complementary polarities of the addends increases, less distortion of addends will be required to reach the transition state. For example, for a high-lying diene HOMO and low-lying dienophile LUMO, the stabilizing HOMO-LUMO interaction will surpass the destabilizing molecular distortion energy quite early along the reaction coordinate. This will clearly favor the concerted mechanism over the step-... 

The fact that Cope rearrangements of alkynes proceed as readily as those of alkenes53 has been puzzling, since it would appear that the transition state would be more easily attained in the case of alkenes. However, our results indicate that considerable bending of the acetylenic units occurs easily in the transition state, since the energy required is counteracted by increased HOMO-LUMO interaction. Thus,... 

It is suggested that steric effects tend to destabilize the antiperiplanar transition state normally associated with the formation of syn adducts in such reactions (Fig. 9). The alternative synclinal arrangement might benefit from favorable HOMO-LUMO interactions (see Fig. 3). 

A more recent study reached a similar conclusion [78]. It was found that cycliza-tions of (Z)- and ( )-3-phenyl-8-tributylstannyl-6-octenal were highly diastereoselec-tive (Fig. 17). The (Z) isomer yielded cis, fra/js-3-phenyl-2-vinylcyclohexanol as the major product (96 4) whereas the (E) isomer afforded the trans, trans isomer (95 5). A favorable HOMO-LUMO interaction was proposed as a decisive factor in stabilizing the favored synclinal transition states. This stabilization is lacking in the alternative synclinal and antiperiplanar transition states, neither of which has the correct geometry for orbital overlap. As in the previous study, the aldehyde and double bond substituents (asterisked carbons in Fig. 17) are unable to attain an anti orientation in the antiperiplanar transition states, as has been proposed for the intermolecular additions. 

This chapter is an introduction to qualitative molecular orbital theory and pericyclic reactions. Pericyclic reactions have cyclic transition states and electron flow paths that appear to go around in a loop. The regiochemistry and stereochemistry of these reactions are usually predictable by HOMO-LUMO interactions, so to understand them we need to understand molecular orbital theory, at least on a qualitative basis. 

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