Lewis acids HOMO-LUMO interactions

In molecular orbital terms, the donation can be viewed as a HOMO-LUMO interaction (Chapter 9). Double hydride bridges, as found in B,H, also are exhibited by bimetallic species such as the chromium anion formed in Eq. 15.18. The sirmlarnv between these two dibridged species is underscored by the fact that their Lewis acid and Lewis base fragments can be interchanged [HCr(CO)sJ reacts with BH, to form 16... 

A cation (or other electrophile) will interact principally with the HOMO of the carbonyl, i.e. the oxygen p lone pair. Hence, if all other interactions are negligible, the optimum geometry for the ate complex should be 17. However, ab initio calculations13 predict structures 18 (if M+ = H+ or Me+) and 19 (if M+ = Li+ or BH2+), where the cation complexes the two lone pairs simultaneously. The bent structure 18 is favored if the Lewis acid has a o acceptor orbital, whereas the linear complex 19 is preferred if an additional rc-type acceptor orbital is available. The HOMO-LUMO interaction is slightly diminished, but this is compensated by the interaction with the s lone pair. 

FIGURE 6-5 HOMO-LUMO Interactions. (Adapted with permission from W. B. Jensen, The Lewis Acid-Base Concepts, Wiley-Interscience, New York, 1980, Figure 4-6, p. 140. Copyright 1980, John Wiley Sons, Inc. Reprinted by permission of John Wiley Sons, Inc.)... 

Four different types of HOMO-LUMO interactions between the reference moiecuie A (HjO) and moiecuie B, where B = Na, Ci , Mg +, or Fj and water is acting as an oxidant, Lewis acid, Lewis base, and... 

A simple approach for the formation of 2-substituted 3,4-dihydro-2H-pyrans, which are useful precursors for natural products such as optically active carbohydrates, is the catalytic enantioselective cycloaddition reaction of a,/ -unsaturated carbonyl compounds with electron-rich alkenes. This is an inverse electron-demand cycloaddition reaction which is controlled by a dominant interaction between the LUMO of the 1-oxa-1,3-butadiene and the HOMO of the alkene (Scheme 4.2, right). This is usually a concerted non-synchronous reaction with retention of the configuration of the die-nophile and results in normally high regioselectivity, which in the presence of Lewis acids is improved and, furthermore, also increases the reaction rate. 

The coordination of the dienophile to a Lewis acid (in the calculations a proton was used as the Lewis acid) leads also to an increase in regioselectivity. The re-gioselectivity of reactions of electron-rich, or conjugated dienes, with electron-deficient dienophiles is also controlled hy the diene HOMO-dienophile LUMO interaction. From Fig. 8.2 it appears that the difference in magnitudes of the LUMO coefficients at carhon atoms 1 and 2 of acrolein (Ci -C2 = 0.20) is smaller than the same difference for protonated acrolein (Ci -C2 = 0.30-0.43) so that the reaction of the latter should he considerable more regioselective than the former in accordance with the experimental results [3]. 

The basic concept of activation in hetero-Diels-Alder reactions is to utilize the lone-pair electrons of the carbonyl and imine functionality for coordination to the Lewis acid. The coordination of the dienophile to the Lewis acid changes the FMOs of the dienophile and for the normal electron-demand reactions a decrease of the LUMO and HOMO energies is observed leading to a better interaction with... 

Lewis acid catalysis enormously enriches the scope of Diels-Alder reactions, but it is limited to reagents containing Lewis basic sites, i.e. functional groups with lone pairs such as carbonyl, amino, ether or nitro close to the reaction centre. As we have seen in the discussion about the FMO aspects of Lewis acids, the major reason for catalysis is the reduction of the HOMO-LUMO gap. In case of Diels-Alder reactions with normal electron demand, it follows that the coordination of the Lewis acid lowers the LUMO energy of the dienophile. Such interactions are only possible if there is a spatial proximity or an electronic conjugation between the coordinated Lewis basic site and the reaction centre. Fortunately, in nearly every Diels-Alder reaction one of the reagents, mostly the dienophile, meets this requirement. 

The effects of Lewis acids on the stereoselectivities can also be understood in terms of orbital interactions. The variation in charge at the respective basic centre gives rise to a change in the magnitude of the orbital coefficients of the entire interacting molecular orbital. These effects are visualized by the HOMO and LUMO representations of the Lewis acid-base complex of acrolein and trifluoroborane (Figure 3), and in an even more extreme case by the HOMO and LUMO representations of one of the simplest dienophile-Lewis acid complexes protonated acrolein92,93. 

These results led to a separation of the observed Diels-Alder reactivities into three categories (a) increase of the rate constants on increasing the Lewis acid character of the solvent as quantified by the AN parameter this behaviour reflects the interactions between the LUMO of the solvent and the HOMO of the reactants and is similar to Lewis acid catalysis (vide supra) (b) reaction retardation by electron donation, as quantified by the D-ji parameter the HOMOsoivent-LUMOreactant interactions are held responsible for this effect, representing an anti-Lewis acid interaction which increases the HOMO-LUMO gap and hence hampers the reaction (c) the Diels-Alder reactions show very small solvent effects and are relatively insensitive to specific reactant-solvent interactions, and... 

Due to the increased reactivity of the reaction in the presence of a Lewis acid, the reaction scope was extended to singly activated alkenes. Previous results had shown either no reaction or extremely poor yields. However, under the Lewis acid catalyzed conditions, acrylonitrile furnished a 1 1, endo/exo mixture of products. The addition of the catalyst gave unexpected regiochemistry in the reaction, which is analogous with results described in Grigg s metal catalyzed reactions. These observations in the reversal of regio- and stereocontrol of the reactions were rationalized by a reversal of the dominant, interacting frontier orbitals to a LUMO dipole-HOMO dipolarophile combination due to the ylide-catalyst complex. This complex resulted in a further withdrawal of electrons from the azomethine ylide. 

Answer. The Lewis acidity depends on the interaction energy ( ) from the interaction of the LUMO of the acid with the HOMO of the nucleophile. The interaction is of a type, with the base HOMO (usually a nonbonded p or spn hybrid) interacting end on with the LUMO, which for the methyl cation is a single 2p orbital and for the allyl system is a linear combination of 2p orbitals. The LUMOs of the two systems are shown below. 

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