Modern density functional theory and powerful contemporary computers have made it possible to explore complex reactions of value in organic synthesis. We describe recent explorations of mechanisms and origins of stereoselectivities with density functional theory calculations. The specific functionals and basis sets that are routinely used in computational studies of stereoselectivities of organic and organometallic reactions in our group are described, followed by our recent studies that uncovered the origins of stereocontrol in reactions catalyzed by (1) vicinal diamines, including cinchona alkaloid-derived primary amines, (2) vicinal amidophosphines, and (3) organo-transition-metal complexes. Two common cyclic models account for the stereoselectivity of aldol reactions of metal enolates (Zimmerman-Traxler) or those catalyzed by the organocatalyst proline (Houk-List). Three other models were derived from computational studies described in this Account.Cinchona alkaloid-derived primary amines and other vicinal diamines are venerable asymmetric organocatalysts. For α-fluorinations and a variety of aldol reactions, vicinal diamines form enamines at one terminal amine and activate electrophilically with NH+ or NF+ at the other. We found that the stereocontrolling transition states are cyclic and that their conformational preferences are responsible for the observed stereoselectivity. In fluorinations, the chair seven-membered cyclic transition states is highly favored, just as the Zimmerman-Traxler chair six-membered aldol transition state controls stereoselectivity. In aldol reactions with vicinal diamine catalysts, the crown transition states are favored, both in the prototype and in an experimental example, shown in the graphic. We found that low-energy conformations of cyclic transition states occur and control stereoselectivities in these reactions. Another class of bifunctional organocatalysts, the vicinal amidophosphines, catalyzes the (3 + 2) annulation reaction of allenes with activated olefins. Stereocontrol here is due to an intermolecular hydrogen bond that activates the electrophilic partner in this reaction. We have also studied complex organometallic catalysts. Krische's ruthenium-catalyzed asymmetric hydrohydroxyalkylation of butadiene involves two chiral ligands at Ru, a chiral diphosphine and a chiral phosphate. The size of this combination strains the limits of modern computations with over 160 atoms, multiple significant steps, and a variety of ligand coordinations and conformations possible. We found that carbon-carbon bond formation occurs via a chair Zimmerman-Traxler-type transition structure and that a formyl CH⋯O hydrogen bond from aldehyde CH to phosphate oxygen, as well as steric interactions of the two chiral ligands, control the stereoselectivity.
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